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Numerical Mathematics and Optimization

Holder of the Chair

Prof. Dr.ChristianKanzow

Holder of the Chair
Chair of Mathematics VII
Emil-Fischer-Straße 30
97074Würzburg
Building: 30 (Mathematik West)
Room: 02.008
Portrait Christian Kanzow

Research Interests

  • Optimization problems
  • Complementarity problems
  • (Quasi-) Variational inequalities
  • (Generalized) Nash equilibrium problems
  • Mathematical programs with equilibrium constraints
  • Sparse optimization
  • Cardinality constraints
  • Algorithms for these classes of problems

 

Publications

Books

 

Book cover          Book cover          Book cover          Book cover

Preprint
Journal Articles

2019

  • Christian Kanzow, Veronika Karl, Daniel Steck, and Daniel Wachsmuth
    The Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach Spaces.
    SIAM Journal on Optimization 29 (1), 2019, pp. 767 - 793  (DOI: 10.1137/17M114114X) ( Preprint )
     
  • Eike Börgens und Christian Kanzow
    Regularized Jacobi-type ADMM-Methods for a Class of Separable Convex Optimization Problems in Hilbert Spaces
    Computational Optimization and Applications, to appear (Preprint)

2018

  • Christian Kanzow and Daniel Steck
    On Error Bounds and Multiplier Methods for Variational Problems in Banach Spaces.
    SIAM Journal on Control and Optimization 56 (3), 2018, pp. 1716 - 1738 (DOI: 10.1137/17M1146518) ( Preprint )
     
  • Eike Börgens and Christian Kanzow
    A Distributed Regularized Jacobi-type ADMM-Method for Generalized Nash Equilibrium Problems in Hilbert Spaces.
    Numerical Functional Analysis and Optimization 39 (12), pp. 1316 - 1349 (DOI: 10.1080/01630563.2018.1477800) (Preprint not available since it is identical to the accepted version)
     
  • Christian Kanzow and Daniel Steck
    Improved Local Convergence Results for Augmented Lagrangian Methods in C2-Cone Reducible Constrained Optimization.
    Mathematical Programming, to appear ( Preprint )
     
  • Christian Kanzow, Daniel Steck, and Daniel Wachsmuth
    An Augmented Lagrangian Method for Optimization Problems in Banach Spaces.
    SIAM Journal on Control and Optimization 56 (1), 2018, pp. 272 - 291 (DOI: 10.1137/16M1107103) ( Preprint ; note that the accepted version contains a few corrections)
     
  • Christian Kanzow and Daniel Steck
    Augmented Lagrangian and Exact Penalty Methods for Quasi-Variational Inequalities.
    Computational Optimization and Applications 69 (3), 2018, pp. 801 - 824 (DOI: 10.1007/s10589-017-9963-0) ( Preprint )
     
  • Christian Kanzow and Yekini Shehu
    Strong Convergence of a Double Projection-type Method for Monotone Variational Inequalities in Hilbert Spaces.
    Journal of Fixed Point Theory and Applications 20:51, 2018 (24 pages) (DOI: 10.1007/s11784-018-0531-8) ( Preprint )
     
  • Leonardo Galli, Christian Kanzow, and Marco Sciandrone
    A Nonmonotone Trust-Region Method for Generalized Nash Equilibrium Problems with Strong Convergence Properties.
    Computational Optimization and Applications 69, 2018, pp. 629 - 652 (DOI: 10.1007/s10589-017-9960-3) ( Preprint )
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2017

  • Christian Kanzow and Daniel Steck
    An Example Comparing the Standard and Safeguarded Augmented Lagrangian Methods.
    Operations Research Letters 45 (6), 2017, 598 - 603 (DOI: 10.1016/j.orl.2017.09.005) ( Preprint )
     
  • Christian Kanzow and Daniel Steck
    A Generalized Proximal-Point Method for Convex Optimization Problems in Hilbert Spaces.
    Optimization 66 (10), 2017, 1667 - 1676 (DOI: 10.1080/02331934.2017.1349127) ( Preprint )
     
  • Christian Kanzow and Yekini Shehu
    Generalized Krasnoselskii-Mann-type Iterations for Nonexpansive Mappings in Hilbert Spaces.
    Computational Optimization and Applications 67 (3), 2017, pp. 595-620 (DOI: 10.1007/s10589-017-9902-0) ( Preprint )

2016

  • Christian Kanzow and Daniel Steck
    Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems.
    SIAM Journal on Optimization 26 (4), 2016, pp. 2034-2058 (DOI: 10.1137/16M1068256) ( Preprint ) ( BibTeX )
     
  • Simone Görner and Christian Kanzow
    On Newton's Method for the Fermat-Weber Location Problem.
    Journal of Optimization Theory and Applications 170 (1), 2016, pp. 107-118 (DOI: 10.1007/s10957-016-0946-6) ( Preprint ) ( BibTeX )
     
  • Michal Červinka, Christian Kanzow, and Alexandra Schwartz
    Constraint Qualifications and Optimality Conditions of Cardinality-Constrained Optimization Problems.
    Mathematical Programming 160 (1), 2016, pp. 353-377 (DOI: 10.1007/s10107-016-0986-6) ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    On the Multiplier-Penalty-Approach for Quasi-Variational Inequalities.
    Mathematical Programming 160 (1), 2016, pp. 33-63 (DOI: 10.1007/s10107-015-0973-3) ( Preprint ) ( BibTeX )
     
  • Oleg P. Burdakov, Christian Kanzow, and Alexandra Schwartz:
    Mathematical Programs with Cardinality Constraints: Reformulation by Complementarity-type Constraints and a Regularization Method.
    SIAM Journal on Optimization 26 (1), 2016, pp. 397-425 (DOI: 10.1137/140978077) ( Preprint ) ( BibTeX )

2015

  • Francisco Facchinei, Christian Kanzow, Sebastian Karl, and Simone Sagratella:
    The Semismooth Newton Method for the Solution of Quasi-Variational Inequalities.
    Computational Optimization and Applications 62 (1), 2015, pp. 85-109 ( Preprint ) ( BibTeX )
     
  • Nadja Harms, Tim Hoheisel, and Christian Kanzow
    On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems.
    Journal of Optimization Theory and Applications 166, 2015, pp. 659-685 ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Alexandra Schwartz:
    The Price of Inexactness: Convergence Properties of Relaxation Methods for Mathematical Programs with Equilibrium Constraints Revisited.
    Mathematics of Operations Research 40, 2015, pp. 253-275 ( Preprint ) ( BibTeX )
     
  • Nadja Harms, Christian Kanzow, and Oliver Stein
    On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems.
    Optimization 64, 2015, pp. 365-388 ( Preprint ) ( BibTeX )

2014

  • Nadja Harms, Tim Hoheisel, and Christian Kanzow
    On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities.
    Journal of Optimization Theory and Applications 163, 2014, pp. 413-438 ( Preprint ) ( BibTeX )
     
  • Jörg Franke, Christian Kanzow, Wolfgang Leininger, and Alexandra Schwartz
    Lottery versus All-Pay Auction Contests: A Revenue Dominance Theorem.
    Games and Economic Behavior 83, 2014, pp. 116-126 ( Preprint ) ( BibTeX )
     
  • Nadja Harms, Christian Kanzow, and Oliver Stein
    Smoothness Properties of a Regularized Gap Function for Quasi-Variational Inequalities.
    Optimization Methods and Software 29, 2014, pp. 720-750 ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Alexandra Schwartz
    Convergence Properties of the Inexact Lin-Fukushima Relaxation Method for Mathematical Programs with Equilibrium Constraints.
    Computational Optimization and Applications 59, 2014, pp. 249-262 ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei, Christian Kanzow, and Simone Sagratella
    Solving Quasi-Variational Inequalities via their KKT-Conditions.
    Mathematical Programming 144, 2014, pp. 369-412 ( Preprint ) ( BibTeX )

2013

  • Christian Kanzow and Alexandra Schwartz
    A New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties.
    SIAM Journal on Optimization 23, 2013, pp. 770-798. ( Preprint ) ( BibTeX )
     
  • Wolfgang Achtziger, Tim Hoheisel, and Christian Kanzow
    A Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints.
    Computational Optimization and Applications 55, 2013, pp. 733-767. ( BibTeX )
     
  • Francisco Facchinei, Christian Kanzow, and Simone Sagratella
    QVILIB: A Library of Quasi-Variational Inequality Test Problems.
    Pacific Journal of Optimization 9, 2013, pp. 225-250. ( Preprint ) ( BibTeX )
     
  • Alfio Borzi and Christian Kanzow
    Formulation and Numerical Solution of Nash Equilibrium Multiobjective Elliptic Control Problems.
    SIAM Journal on Control and Optimization 51, 2013, pp. 718-744 ( Preprint ) ( BibTeX )
     
  • Axel Dreves, Anna von Heusinger, Christian Kanzow, and Masao Fukushima
    A Globalized Newton Method for the Computation of Normalized Nash Equilibria.
    Journal of Global Optimization 56, 2013, pp. 327-340 ( Preprint ) ( BibTeX )
     
  • James V. Burke, Tim Hoheisel, and Christian Kanzow
    Gradient Consistency for Integral-Convolution Smoothing Functions.
    Set-Valued and Variational Analysis 21, 2013, pp. 359-376 ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz
    Theoretical and Numerical Comparison of Relaxation Methods for Mathematical Programs with Complementarity Constraints.
    Mathematical Programming 137, 2013, pp. 257-288 ( Preprint ) ( BibTeX )
     
  • Jörg Franke, Christian Kanzow, Wolfgang Leininger, and Alexandra Schwartz
    Effort Maximization in Asymmetric Contest Games with Heterogeneous Contestants.
    Economic Theory 52, 2013, pp. 589-630 ( Preprint )  ( BibTeX ) (note that the published paper is a significant improvement of the preprint version).

2012

  • Michael Brückner, Christian Kanzow, and Tobias Scheffer
    Static Prediction Games for Adversarial Learning Problems.
    Journal of Machine Learning Research 13, 2012, pp. 2617-2654 ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz:
    Mathematical Programs with Vanishing Constraints: A New Regularization Approach with Strong Convergence Properties.
    Optimization 61, 2012, pp. 619-636 ( Preprint ) ( BibTeX )
     
  • Wolfgang Achtziger, Christian Kanzow, and Tim Hoheisel:
    On a relaxation method for mathematical programs with vanishing constraints.
    GAMM-Mitteilungen 35, 2012, pp. 110-130. ( BibTeX )
     
  • Axel Dreves, Christian Kanzow, and Oliver Stein
    Nonsmooth Optimization Reformulations of Player Convex Generalized Nash Equilibrium Problems.
    Journal of Global Optimization 53, 2012, pp. 587-614 ( Preprint ) ( BibTeX )
     
  • Anna von Heusinger, Christian Kanzow, and Masao Fukushima
    Newton's Method for Computing a Normalized Equilibrium in the Generalized Nash Game through Fixed Point Formulation.
    Mathematical Programming 132, 2012, pp. 99-123. ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz
    Convergence of a Local Regularization Approach for Mathematical Programs with Complementarity or Vanishing Constraints.
    Optimization Methods and Software 27, 2012, pp. 483-512. ( Preprint ) ( BibTeX )
     
  • Hannes Buchholzer and Christian Kanzow
    Bounds for the Extremal Eigenvalues of a Class of Symmetric Tridiagonal Matrices with Applications.
    Linear Algebra and its Applications 436, 2012, pp. 1837-1849 ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, Boris S. Mordukhovich, and Hung Phan
    Generalized Newton's Method Based on the Graphical Derivative.
    Nonlinear Analysis: Theory, Methods, and Applications 75, 2012, pp. 1324-1340. ( Preprint ) ( BibTeX )

2011

  • Axel Dreves, Francisco Facchinei, Christian Kanzow, and Simone Sagratella
    On the Solution of the KKT Conditions of Generalized Nash Equilibrium Problems.
    SIAM Journal on Optimization 21, 2011, pp. 1082-1108. ( Preprint ) ( BibTeX )
     
  • Hannes Buchholzer, Christian Kanzow, Peter Knabner, and Serge Kräutle
    Solution of Reactive Transport Problems Including Mineral Precipitation-Dissolution Reactions by a Semismooth Newton Method.
    Computational Optimization and Applications 50, 2011, pp. 193-221. ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz
    Improved Convergence Properties of the Lin-Fukushima-Regularization Method for Mathematical Programs with Complementarity Constraints.
    Numerical Algebra, Control, and Optimization 1, 2011, 49-60 ( Preprint ) ( BibTeX )
     
  • Axel Dreves and Christian Kanzow
    Nonsmooth Optimization Reformulations Characterizing all Solutions of Jointly Convex Generalized Nash Equilibrium Problems.
    Computational Optimization and Applications 50, 2011, 23-48. ( Preprint ) ( BibTeX )

2010

  • Christian Kanzow and Alexandra Schwartz
    Mathematical Programs with Equilibrium Constraints: Enhanced Fritz John-Conditions, New Constraint Qualifications and Improved Exact Penalty Results.
    SIAM Journal on Optimization 20, 2010, 2730-2753. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    Penalty Methods for the Solution of Generalized Nash Equilibrium Problems.
    SIAM Journal on Optimization 20, 2010, 2228-2253. Preprint (including a detailed description of all test examples which are not published in the SIOPT paper) ( BibTeX )
     
  • Tim Hoheisel, Christian Kanzow, and Jiri V. Outrata
    Exact Penalty Results for Mathematical Programs with Vanishing Constraints.
    Nonlinear Analysis: Theory, Methods, and Applications 72, 2010, 2514-2526. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    Generalized Nash Equilibrium Problems.
    Annals of Operations Research 175, 2010, 177-211 ( Preprint ) (this is an updated version of the survey paper that appeared in 4OR, 5 (3), 173-210 (2007)). ( BibTeX )

2009

  • Christian Kanzow, Izabella Ferenczi, and Masao Fukushima
    On the Local Convergence of Semismooth Newton Methods for Linear and Nonlinear Second-Order Cone Programs Without Strict Complementarity.
    SIAM Journal on Optimization 20, 2009, 297-320. ( Preprint ) ( BibTeX )
     
  • Anna von Heusinger and Christian Kanzow
    Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search.
    Journal of Optimization Theory and Applications 143, 2009, 159-183. ( Preprint ) ( BibTeX )
     
  • Anna von Heusinger and Christian Kanzow
    Optimization Reformulations of the Generalized Nash Equilibrium Problem Using Nikaido-Isoda-Type Functions.
    Computational Optimization and Applications 43, 2009, pp. 353-377. ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel and Christian Kanzow
    On the Abadie and Guignard Constraint Qualifications for Mathematical Programmes with Vanishing Constraints.
    Optimization 58, 2009, pp. 431-448. ( Preprint ) ( BibTeX )

2008

  • Anna von Heusinger and Christian Kanzow
    SC1 Optimization Reformulations of the Generalized Nash Equilibrium Problem.
    Optimization Methods and Software 23, 2008, pp. 953-973 ( Preprint ) ( BibTeX )
     
  • Amir Beck, Aharon Ben-Tal, and Christian Kanzow
    A Fast Method for Finding the Global Solution of the Regularized Structured Total Least Squares Problem for Image Deblurring.
    SIAM Journal on Matrix Analysis and Applications 30, 2008, pp. 419-443 ( Preprint ) ( BibTeX )
     
  • Wolfgang Achtziger and Christian Kanzow
    Mathematical Programs with Vanishing Constraints: Optimality Conditions and Constraint Qualifications.
    Mathematical Programming 114, 2008, pp. 69-99. ( Preprint ) ( BibTeX )
     
  • Tim Hoheisel and Christian Kanzow
    Stationary Conditions for Mathematical Programs with Vanishing Constraints Using Weak Constraint Qualifications.
    Journal of Mathematical Analysis and Applications 337, 2008, pp. 292-310. ( Preprint ) ( BibTeX )

2007

  • Tim Hoheisel and Christian Kanzow
    First- and Second-Order Optimality Conditions for Mathematical Programs with Vanishing Constraints.
    Applications of Mathematics 52, 2007, pp. 495-514 (special issue dedicated to J.V. Outrata's 60. birthday) ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    Generalized Nash Equilibrium Problems.
    4OR - A Quarterly Journal of Operations Research 5, 2007, pp. 173-210. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Stefania Petra
    Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems.
    Optimization Methods and Software 22, 2007, pp. 713-735. ( Preprint ) ( BibTeX )
     
  • Michael L. Flegel and Christian Kanzow
    Equivalence of two nondegeneracy conditions for semidefinite programs.
    Journal of Optimization Theory and Applications 135, 2007, pp. 381-397. ( Preprint ) ( BibTeX )
     
  • Michael L. Flegel, Christian Kanzow, and Jiri V. Outrata
    Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints.
    Set-Valued Analysis 15, 2007, pp. 139-162. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Andreas Klug
    An interior-point affine-scaling trust-region method for semismooth equations with box constraints.
    Computational Optimization and Applications 37, 2007, pp. 329-353. ( Preprint ) ( BibTeX )

2006

  • Christian Kanzow and Andreas Klug
    On affine-scaling interior-point Newton methods for nonlinear minimization with bound constraints.
    Computational Optimization and Applications 35, 2006, pp. 177-197. ( Preprint ) ( BibTeX )

2005

  • Michael L. Flegel and Christian Kanzow
    On the Guignard constraint qualification for mathematical programs with equilibrium constraints.
    Optimization 54, 2005, pp. 517-534. ( Preprint ) ( BibTeX )
     
  • Michael L. Flegel and Christian Kanzow
    On M-stationary points for mathematical programs with equilibrium constraints.
    Journal of Mathematical Analysis and Applications 310, 2005, pp. 286-302. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow, Christian Nagel, Hirokazu Kato and Masao Fukushima
    Successive linearization methods for nonlinear semidefinite programs.
    Computational Optimization and Applications 31, 2005, pp. 251-273. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Christian Nagel
    Quadratic convergence of a Newton-type method for semidefinite programs without strict complementarity.
    SIAM Journal on Optimization 15, 2005, pp. 654-672. ( Preprint ) ( BibTeX )
     
  • Michael L. Flegel and Christian Kanzow
    Abadie-type constraint qualification for mathematical programs with equilibrium constraints.
    Journal of Optimization Theory and Applications 124, 2005, pp. 595-614. ( Preprint ) ( BibTeX )

2004

  • Christian Kanzow, Nobuo Yamashita and Masao Fukushima
    Levenberg-Marquardt methods for constrained nonlinear equations with strong local convergence properties.
    Journal of Computational and Applied Mathematics 172, 2004, pp. 375-397. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Stefania Petra
    On a semismooth least squares formulation of complementarity problems with gap reduction.
    Optimization Methods and Software 19, 2004, pp. 507-525. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Christian Nagel
    Some structural properties of a Newton-type method for semidefinite programs.
    Journal of Optimization Theory and Applications 122, 2004, pp. 219-226. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    Inexact semismooth Newton methods for large-scale complementarity problems.
    Optimization Methods and Software 19, 2004, pp. 309-325. ( Preprint ) ( BibTeX )

2003

  • Michael L. Flegel and Christian Kanzow
    A Fritz John approach to first order optimality conditions for mathematical programs with equilibrium constraints.
    Optimization 52, 2003, pp. 277-286. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Christian Nagel
    Semidefinite programs: New search directions, smoothing-type methods, and numerical results.
    SIAM Journal on Optimization 13, 2003, pp. 1-23 ( Preprint ) ( BibTeX ) (Erratum in SIAM Journal on Optimization 14, 2004, pp. 936-937 ( Preprint )).
     
  • Christian Kanzow, Houduo Qi and Liqun Qi
    On the minimum norm solution of linear programs.
    Journal of Optimization Theory and Applications 116, 2003, pp. 333-345. ( Preprint ) ( BibTeX )

2002

  • Stephan Engelke and Christian Kanzow
    Predictor-corrector smoothing methods for linear programs with a more flexible update of the smoothing parameter.
    Computational Optimization and Applications 23, 2002, pp. 299-320. ( Preprint ) ( BibTeX )
     
  • Stephan Engelke and Christian Kanzow
    Improved smoothing-type methods for the solution of linear programs.
    Numerische Mathematik 90, 2002, pp. 487-507. ( Preprint ) ( BibTeX )

2001

  • Todd S. Munson, Francisco Facchinei, Michael C. Ferris, Andreas Fischer and Christian Kanzow
    The semismooth algorithm for large scale complementarity problems.
    INFORMS Journal on Computing 13, 2001, pp. 294-311. ( Preprint ) ( BibTeX )
     
  • Nobuo Yamashita, Christian Kanzow, Tomoyuki Morimoto and Masao Fukushima
    An infeasible interior proximal method for convex programming problems with linear constraints.
    Journal of Nonlinear and Convex Analysis 2, 2001, pp. 139-156. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    Strictly feasible equation-based methods for mixed complementarity problems.
    Numerische Mathematik 89, 2001, pp. 135-160. ( Preprint ) ( BibTeX )
     
  • Stephan Engelke and Christian Kanzow
    On the solution of linear programs by Jacobian smoothing methods.
    Annals of Operations Research 103, 2001, pp. 49-70. ( Preprint ) ( BibTeX )

2000

  • Bintong Chen, Xiaojun Chen and Christian Kanzow
    A penalized Fischer-Burmeister NCP-function.
    Mathematical Programming 88, 2000, pp. 211-216. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei, Andreas Fischer and Christian Kanzow
    On the identification of zero variables in an interior-point framework.
    SIAM Journal on Optimization 10, 2000, pp. 1058-1078. ( Preprint , sorry, there is a missing graphic in the preprint) ( BibTeX )
     
  • Tecla De Luca, Francisco Facchinei and Christian Kanzow
    A theoretical and numerical comparison of some semismooth algorithms for complementarity problems.
    Computational Optimization and Applications 16, 2000, pp. 173-205. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    Global optimization techniques for mixed complementarity problems.
    Journal of Global Optimization 16, 2000, pp. 1-21. ( Preprint ) ( BibTeX )

1999

  • Michael C. Ferris, Christian Kanzow and Todd S. Munson
    Feasible descent algorithms for mixed complementarity problems.
    Mathematical Programming 86, 1999, pp. 475-497. ( Preprint ) ( BibTeX )
     
  • Ji-Ming Peng, Christian Kanzow and Masao Fukushima
    A hybrid Newton method for solving box constrained variational inequality problems via the D-gap function.
    Optimization Methods and Software 10, 1999, pp. 687-710. ( BibTeX )
     
  • Christian Kanzow and Heiko Pieper
    Jacobian smoothing methods for nonlinear complementarity problems.
    SIAM Journal on Optimization 9, 1999, pp. 342-372. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Houduo Qi
    A QP-free constrained Newton-type method for variational inequality problems.
    Mathematical Programming 85, 1999, pp. 81-106. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    Beyond monotonicity in regularization methods for complementarity problems.
    SIAM Journal on Control and Optimization 37, 1999, pp. 1150-1161. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei, Andreas Fischer, Christian Kanzow and Ji-Ming Peng
    A simply constrained optimization reformulation of KKT systems arising from variational inequalities.
    Applied Mathematics and Optimization 40, 1999, pp. 19-37. ( Preprint ) ( BibTeX )
     
  • Francisco Facchinei, Andreas Fischer and Christian Kanzow
    On the accurate identification of active constraints.
    SIAM Journal on Optimization 9, 1999, pp. 14-32. ( Preprint ) ( BibTeX )

1998

  • Christian Kanzow and Helmut Kleinmichel
    A new class of semismooth Newton-type methods for nonlinear complementarity problems.
    Computational Optimization and Applications 11, 1998, pp. 227-251. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Masao Fukushima
    Solving box constrained variational inequality problems by using the natural residual with D-gap function globalization.
    Operations Research Letters 23, 1998, pp. 45-51. ( BibTeX )
     
  • Christian Kanzow
    An inexact QP-based method for nonlinear complementarity problems.
    Numerische Mathematik 80, 1998, pp. 557-577. ( BibTeX )
     
  • Francisco Facchinei, Andreas Fischer and Christian Kanzow
    Regularity properties of a semismooth reformulation of variational inequalities.
    SIAM Journal on Optimization 8, 1998, pp. 850-869. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow and Masao Fukushima
    Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities.
    Mathematical Programming 83, 1998, pp. 55-87. ( BibTeX )
     
  • Christian Kanzow and Houyuan Jiang
    A continuation method for (strongly) monotone variational inequalities.
    Mathematical Programming 81, 1998, pp. 103-125. ( Preprint ) ( BibTeX )

1997

  • Christian Kanzow
    A new approach to continuation methods for complementarity problems with uniform P-functions.
    Operations Research Letters 20, 1997, pp. 85-92. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow, Nobuo Yamashita and Masao Fukushima
    New NCP-functions and their properties.
    Journal of Optimization Theory and Applications 94, 1997, pp. 115-135. ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems.
    Mathematical Programming 76, 1997, pp. 493-512. ( BibTeX )
     
  • Francisco Facchinei and Christian Kanzow
    On unconstrained and constrained stationary points of the implicit Lagrangian.
    Journal of Optimization Theory and Applications 92, 1997, pp. 99-115. ( Preprint ) ( BibTeX )

1996

  • Tecla De Luca, Francisco Facchinei and Christian Kanzow
    A semismooth equation approach to the solution of nonlinear complementarity problems.
    Mathematical Programming 75, 1996, pp. 407-439. ( BibTeX )
     
  • Andreas Fischer and Christian Kanzow
    On finite termination of an iterative method for linear complementarity problems.
    Mathematical Programming 74, 1996, pp. 279-292. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    Some noninterior continuation methods for linear complementarity problems.
    SIAM Journal on Matrix Analysis and Applications 17, 1996, pp. 851-868. ( BibTeX )
     
  • Christian Kanzow and Masao Fukushima
    Equivalence of the generalized complementarity problem to differentiable unconstrained minimization.
    Journal of Optimization Theory and Applications 90, 1996, pp. 581-603. ( BibTeX )
     
  • Carl Geiger and Christian Kanzow
    On the resolution of monotone complementarity problems.
    Computational Optimization and Applications 5, 1996, pp. 155-173. ( Preprint ) ( BibTeX )
     
  • Christian Kanzow
    Global convergence properties of some iterative methods for linear complementarity problems.
    SIAM Journal on Optimization 6, 1996, pp. 326-341. ( BibTeX )
     
  • Christian Kanzow
    Nonlinear complementarity as unconstrained optimization.
    Journal of Optimization Theory and Applications 88, 1996, pp. 139-155. ( BibTeX )

1995

  • Christian Kanzow and Helmut Kleinmichel
    A class of Newton-type methods for equality and inequality constrained optimization.
    Optimization Methods and Software 5, 1995, pp. 173-198. ( BibTeX )

1994

  • Christian Kanzow
    An unconstrained optimization technique for large-scale linearly constrained convex minimization problems.
    Computing 53, 1994, pp. 101-117. ( BibTeX )
     
  • Christian Kanzow
    Some equation-based methods for the nonlinear complementarity problem.
    Optimization Methods and Software 3, 1994, pp. 327-340. ( BibTeX )
Articles in Refereed Proceedings
  • Oleg Burdakov, Christian Kanzow, and Alexandra Schwartz
    On a reformulation of mathematical programs with cardinality constraints.
    In: D.Y. Gao, N. Ruan, and W.X. Xing (eds.): Advances in Global Optimization. Proceedings of the third World Congress of Global Optimization, July 8-12, 2013, Huangshan, China. Springer, 2015, pp. 3-14.
     
  • Michael L. Flegel and Christian Kanzow
    A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints.
    In: S. Dempe and V. Kalashnikov (eds.): Optimization with Multivalued Mappings: Theory, Applications and Algorithms. Springer, New York, NY, 2006, pp. 111-122. ( Preprint )
     
  • Christian Kanzow
    Proximal-like methods for convex minimization problems.
    In: L. Qi, K.L. Teo and X.Q. Yang (eds.): Optimization and Control with Applications. Springer, New York, NY, 2005, pp. 369-392.
     
  • Michael C. Ferris and Christian Kanzow
    Complementarity and related problems.
    In: P.M. Pardalos and M.G.C. Resende (eds.): Handbook of Applied Optimization. Oxford University Press, New York, NY, 2002, pp. 514-530.
     
  • Christian Kanzow
    An active set-type Newton method for constrained nonlinear systems.
    In: M.C. Ferris, O.L. Mangasarian and J.-S. Pang (eds.): Complementarity: Applications, Algorithms and Extensions. Kluwer Academic Publishers, 2001, pp. 179-200.
     
  • Christian Kanzow and Martin Zupke
    Inexact trust-region methods for nonlinear complementarity problems.
    In: M. Fukushima and L. Qi (eds.): Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Kluwer Academic Press, Dordrecht, The Netherlands, 1999, pp. 211-233.
     
  • Francisco Facchinei, Andreas Fischer and Christian Kanzow
    A semismooth Newton method for variational inequalities: The case of box constraints.
    In: M.C. Ferris and J.-S. Pang (eds.): Complementarity and Variational Problems: State of the Art. SIAM, Philadelphia, 1997, pp. 76-90.
     
  • Francisco Facchinei, Andreas Fischer and Christian Kanzow
    Inexact Newton methods for semismooth equations with applications to variational inequality problems.
    In: G. Di Pillo and F. Giannessi (eds.): Nonlinear Optimization and Applications. Plenum Press, New York, 1996, pp. 125-139.
Diploma Thesis / Ph.D. Thesis / Habilitation Thesis

Diploma Thesis

Christian Kanzow
Newton-Typ-Verfahren in der restringierten Optimierung.
Institute of Applied Mathematics, University of Hamburg, Hamburg, November 1991 (in German).


Ph.D. Thesis

Christian Kanzow
C-Funktionen und ihre Anwendung auf restringierte Optimierungsaufgaben und Komplementaritätsprobleme.
Verlag an der Lottbek, Ammersbek, January 1995 (in German).


Habilitation Thesis

Christian Kanzow
Semismooth Newton-type Methods for the Solution of Nonlinear Complementarity Problems.
Institute of Applied Mathematics, University of Hamburg, Hamburg, April 1997.

Further Information

Curriculum Vitae

Studies

1987-1989 at the University of Kiel, Germany
1989-1992 at the University of Hamburg, Germany


Degrees

1992 Diploma in Mathematics at the University of Hamburg
1995 Ph.D. in Mathematics at the University of Hamburg
1997 Habilitation in Mathematics at the University of Hamburg


Positions

1992-1995 "Wissenschaftlicher Mitarbeiter" at the University of Hamburg
1995-2001 "Wissenschaftlicher Assistent" at the University of Hamburg
2001-today Full Professor at the University of Würzburg


Research Stays

1997-1998 at the University of Wisconsin in Madison, USA
1998-1999 at the Università di Roma "La Sapienza" in Rome, Italy
Several shorter research stays in Kyoto, Sydney, Rome etc.


"Vertretungsprofessur"

1999-2000 "Vertretungsprofessur" at the University of Trier


Scientific Awards

Kurt-Hartwig-Siemers-Preis 1995 for excellent Ph.D. Thesis
Charles Broyden Prize 2008: Best paper award from the journal "Optimization Methods and Software"
UTIA Best Paper Award 2010 (2nd prize), Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic


Marital Status

Married to Karin Kanzow since 1988. We have three kids:
Rainer Kanzow (born 1993)
Florian Kanzow (born 1994)
Christoph Kanzow (born 1996)

Positions

Faculty management

  • Dean of Faculty of Mathematics and Computer Science (1. October 2017 to 30. September 2019)
  • Vice Dean of Faculty of Mathematics and Computer Science (1. October 2015 to 30. September 2017)

Fellowship in university committees

  • Faculty council (several times)
  • Extended Executive Board (2017 - 2019)
  • Concilium Decanale
  • Presidencies of various appointment committees
Hobby

Although there is not much time for other interests than mathematics and the family, I try to do at least one additional thing in order to have some kind of compensation to the work in the office and at home, and that's cycling. From time to time, I take part in some races close to my living area (this used to be Hamburg till September 2001 and is Würzburg since October 2001). Here are some of my recent results:

  • HEW Cyclassics, Hamburg, 166 km in about 4h 53min (August 1999, cold and windy weather)
  • HEW Cyclassics, Hamburg, 166 km in about 4h 25min (August 2000, perfect weather)
  • Deutschland-Tour Hamburg-Uelzen, 96 km in about 2h 26min (May 2001, cold and stormy weather)
  • HEW Cyclassics, Hamburg, 166 km in about 4h 14min (August 2001, perfect weather)
  • Deutschland-Tour Wiesbaden-Erbach, 106 km in about 3h 01min (June 2002, hot weather and hilly area)
  • Rund um den Henninger Turm (Frankfurt), 83,3 km in about 2h 20min (May 2003, windy weather and hilly area)
  • Deutschland-Tour Todtmoos-Feldberg, 87 km in about 3h 10min (June 2003, through the black forest with a lot of mountains)
  • GP Schwarzwald, 120 km around Triberg, accident after 84 km (August 2003, again through the black forest with a lot of mountains)
  • Deutschland-Tour Schöneck-Fichtelberg, 80 km in about 2h 59min (June 2004, through the Erzgebirge with a lot of mountains, rainy weather)

Apart from these races, I also take part in some so-called RTFs (Rad-Touren-Fahrten). These RTFs are no official races, there is no official timing, ranking etc. Some of my recent RTFs are:

  • Quer durch Mainfranken, 165 km around Würzburg (June 2002)
  • Bocksbeuteltour, 120 km around Kitzingen (September 2002)
  • Quer durch Mainfranken, 165 km around Würzburg (June 2003)
  • Quer durch Mainfranken, 165 km around Würzburg (June 2004)
  • Rhöner Kuppenritt, 220 km from Bad Neustadt through the Rhön mountains (July 2004; 3500 m difference in altitude)
  • GP Schwarzwald Triberg, 258 km through the black forest with a lot of mountains including Kandel, Schauinsland, Belchen, and Feldberg (August 2004; 5300 m difference in altitude)
  • Bocksbeuteltour, 120 km around Kitzingen (September 2004)
  • RTF Herbsthausen, 155 km around Bad Mergentheim and Rothenburg o.d. Tauber (May 2005)
  • RTF Frankenhammer, 225 km from Fürth to the Fränkische Schweiz and back with many steep hills (June 2005; 3000 m difference in altitude)
  • Rhöner Kuppenritt, 220 km from Bad Neustadt through the Rhön mountains (July 2005; 3500 m difference in altitude)
  • SURM (Schwarzwald Ultra Rad-Marathon), 230 km through the Black Forest with a lot of mountains including Kandel etc. (September 2005; 3500 m difference in altitude)
  • Rhön Radmarathon (Super Cup), 210 km from Bimbach through the Rhön mountains (June 2006; 3500 m difference in altitude)
  • Rhöner Kuppenritt, 220 km from Bad Neustadt through the Rhön mountains (July 2006; 3500 m difference in altitude)
  • SymBadischer Radmarathon (Super Cup), 201 km from Altdorf through the black forrest (September 2006; 3700 m difference in altitude)
  • GP Triberg Schwarzwald, 258 km through the black forest with a lot of mountains including Kandel, Schauinsland, Belchen, and Feldberg (June 2007; 5300 m difference in altitude)
  • Rhöner Kuppenritt, 220 km from Bad Neustadt through the Rhön mountains (July 2007; 3500 m difference in altitude)
  • Bocksbeuteltour, 162 km around Kitzingen (September 2009)
  • Rhöner Kuppenritt, 220 km from Bad Neustadt through the Rhön mountains (July 2010; 3500 m difference in altitude)
  • 300 km tour around Würzburg with the local club, RSG Würzburg (August 2010)
  • Rhön Radmarathon Extreme (Super Cup), 238 km from Bimbach through the Rhön mountains (June 2011; 4300 m difference in altitude)
  • 300 km tour around Würzburg with the local club, RSG Würzburg (August 2011)
  • Rhön Radmarathon Extreme (Super Cup), 238 km from Bimbach through the Rhön mountains (May 2012; 4300 m difference in altitude)
  • Bocksbeuteltour, 162 km around Kitzingen (September 2012)
  • SURM (Schwarzwald Ultra Rad-Marathon), 233 km through the black forest with a lot of mountains including Kandel etc. (September 2012; 3800 m difference in altitude)
  • Rhön Radmarathon Extreme (Super Cup), 238 km from Bimbach through the Rhön mountains (May 2013; 4400 m difference in altitude)
  • Rhöner Kuppenritt, 205 km from Bad Neustadt through the Rhön mountains (July 2013, 3300 m difference in altitude)
  • Bayerisch-Hessische Grenzfahrt, 205 km (at least officially) from Wenigumstadt through the Odenwald mountains (May 2014, 2200 m difference in altitude)
  • 300 km tour around Würzburg with the local club, RSG Würzburg (August 2014)
  • Bocksbeuteltour, 155 km around Kitzingen (September 2014)
  • SURM (Schwarzwald Ultra Rad-Marathon), 237 km through the black forest with a lot of mountains including Kandel etc. (September 2014; 3800 m difference in altitude; heavy rain and thunderstorms, no fun!)
  • Rhön Radmarathon Extreme² (Super Cup), 248 km from Bimbach through the Rhön mountains (May 2015; 4800 m difference in altitude)
  • Rhöner Kuppenritt, 205 km through the Rhön mountains (July 2015; 3600 m difference in altitude)
  • Bocksbeuteltour, 155 km around Kitzingen (September 2015)
  • SURM (Schwarzwald Ultra Rad-Marathon), 237 km through the black forest with a lot of mountains including Kandel etc. (September 2015; 3800 m difference in altitude)
  • RTF Herbsthausen, 155 km around Bad Mergentheim and Neuenstein (May 2017)
  • Rhöner Kuppenritt, 205 km through the Rhön mountains (July 2017; 3600 m difference in altitude)
  • Arber Radmarathon, 250 km from Regensburg through the Bavarian Forest and back (July 2017; 3750 m difference in altitude)
  • 300 km tour around Würzburg with the local club, RSG Würzburg (August 2017)
  • SURM (Schwarzwald Ultra Rad-Marathon), 237 km through the black forest with a lot of mountains including Kandel etc. (September 2017; 3800 m difference in altitude)
  • Rhön Radmarathon Extreme (Super Cup), 258 km from Bimbach through the Rhön mountains (May 2018; 4700 m difference in altitude)
  • Franken-Tour, 160 km from Ochsenfurt to and around the Tauber valley (June 2018)
  • Rhöner Kuppenritt, 205 km through the Rhön mountains (July 2018; 3600 m difference in altitude; cold and rainy weather)
  • Arber Radmarathon, 250 km from Regensburg through the Bavarian Forest and back (July 2018; 3750 m difference in altitude)
  • Bocksbeuteltour, 215 km around Kitzingen (September 2018, 2100 m difference in altitude)
  • SURM (Schwarzwald Ultra Rad-Marathon), 237 km through the black forest with a lot of mountains including Kandel etc. (September 2018; 3800 m difference in altitude)

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Contact

Lehrstuhl für Mathematik VII (Numerische Mathematik und Optimierung)
Emil-Fischer-Straße 30
Campus Hubland Nord
97074 Würzburg

Phone: +49 931 31-85042
Email

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