Christian Kanzow

Publications

Books

• Carl Geiger and Christian Kanzow: Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben. Springer-Verlag, 1999, 349+xiv pages (in German).

• Carl Geiger and Christian Kanzow: Theorie und Numerik restringierter Optimierungsaufgaben. Springer-Verlag, 2002, 487+xii pages (in German).

• Christian Kanzow: Numerik linearer Gleichungssysteme: Direkte und iterative Verfahren. Springer-Verlag, 2005, 349+xiv pages (in German).

Preprints

• Francisco Facchinei, Christian Kanzow, and Simone Sagratella: QVILIB: A Library of Quasi-Variational Inequality Test Problems. Preprint 308, Institute of Mathematics, University of Würzburg, Würzburg, March 2012.

• Nadja Harms, Christian Kanzow, and Oliver Stein: On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems. Preprint 307, Institute of Mathematics, University of Würzburg, Würzburg, March 2012.

• Alfio Borzi and Christian Kanzow: Formulation and Numerical Solution of Nash Equilibrium Multiobjective Elliptic Control Problems. Preprint 306, Institute of Mathematics, University of Würzburg, Würzburg, February 2012.

• Francisco Facchinei, Christian Kanzow, and Simone Sagratella: Solving Quasi-Variational Inequalities via their KKT-Conditions. Preprint 305, Institute of Mathematics, University of Würzburg, Würzburg, January 2012.

• Michael Brückner, Christian Kanzow, and Tobias Scheffer: Static Prediction Games for Adversarial Learning Problems. Preprint 304, Institute of Mathematics, University of Würzburg, Würzburg, August 2011.

• Christian Kanzow and Alexandra Schwartz: A New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties. Preprint 296, Institute of Mathematics, University of Würzburg, Würzburg, June 2010.

• Wolfgang Achtziger, Tim Hoheisel, and Christian Kanzow: A Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints. Preprint 284, Institute of Mathematics, University of Würzburg, Würzburg, November 2008.

Journal Articles

Below is a list of my journal articles in reversed chronological order. What can be downloaded from this page are the preprint versions of most of these articles. Please note, however, that these preprints sometimes differ substantially from the published papers.

• 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, to appear. ( Preprint)

• Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz: Theoretical and Numerical Comparison of Relaxation Methods for Mathematical Programs with Complementarity Constraints. Mathematical Programming, to appear. ( Preprint )

• Tim Hoheisel, Christian Kanzow, and Alexandra Schwartz: Mathematical Programs with Vanishing Constraints: A New Regularization Approach with Strong Convergence Properties. Optimization, to appear. ( Preprint )

• Jörg Franke, Christian Kanzow, Wolfgang Leininger, and Alexandra Schwartz: Effort Maximization in Asymmetric Contest Games with Heterogeneous Contestants. Economic Theory, to appear. ( Preprint ) (note that the published paper is a significant improvement of the preprint version)

• Axel Dreves, Christian Kanzow, and Oliver Stein: Nonsmooth Optimization Reformulations of Player Convex Generalized Nash Equilibrium Problems. Journal of Global Optimization, to appear. ( Preprint )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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)

• 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 )

• 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)).

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• Wolfgang Achtziger and Christian Kanzow: Mathematical Programs with Vanishing Constraints: Optimality Conditions and Constraint Qualifications. Mathematical Programming 114, 2008, pp. 69-99. ( Preprint )

• 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 )

• 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 )

• Francisco Facchinei and Christian Kanzow: Generalized Nash Equilibrium Problems. 4OR - A Quarterly Journal of Operations Research 5, 2007, pp. 173-210. ( Preprint )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• Michael L. Flegel and Christian Kanzow: On the Guignard constraint qualification for mathematical programs with equilibrium constraints. Optimization 54, 2005, pp. 517-534. ( Preprint )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• 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 )

• Christian Kanzow: Inexact semismooth Newton methods for large-scale complementarity problems. Optimization Methods and Software 19, 2004, pp. 309-325. ( Preprint )

• 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 )

• 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 ) (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 )

• 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 )

• Stephan Engelke and Christian Kanzow: Improved smoothing-type methods for the solution of linear programs. Numerische Mathematik 90, 2002, pp. 487-507. ( Preprint )

• 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 )

• 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 )

• Christian Kanzow: Strictly feasible equation-based methods for mixed complementarity problems. Numerische Mathematik 89, 2001, pp. 135-160. ( Preprint )

• 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 )

• Bintong Chen, Xiaojun Chen and Christian Kanzow: A penalized Fischer-Burmeister NCP-function. Mathematical Programming 88, 2000, pp. 211-216. ( Preprint )

• 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)

• 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 )

• Christian Kanzow: Global optimization techniques for mixed complementarity problems. Journal of Global Optimization 16, 2000, pp. 1-21. ( Preprint )

• Michael C. Ferris, Christian Kanzow and Todd S. Munson: Feasible descent algorithms for mixed complementarity problems. Mathematical Programming 86, 1999, pp. 475-497. ( Preprint )

• 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.

• Christian Kanzow and Heiko Pieper: Jacobian smoothing methods for nonlinear complementarity problems. SIAM Journal on Optimization 9, 1999, pp. 342-372. ( Preprint )

• Christian Kanzow and Houduo Qi: A QP-free constrained Newton-type method for variational inequality problems. Mathematical Programming 85, 1999, pp. 81-106. ( Preprint )

• 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 )

• 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 )

• Francisco Facchinei, Andreas Fischer and Christian Kanzow: On the accurate identification of active constraints. SIAM Journal on Optimization 9, 1999, pp. 14-32. ( Preprint )

• 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 )

• 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.

• Christian Kanzow: An inexact QP-based method for nonlinear complementarity problems. Numerische Mathematik 80, 1998, pp. 557-577.

• 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 )

• 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.

• Christian Kanzow and Houyuan Jiang: A continuation method for (strongly) monotone variational inequalities. Mathematical Programming 81, 1998, pp. 103-125. ( Preprint )

• Christian Kanzow: A new approach to continuation methods for complementarity problems with uniform P-functions. Operations Research Letters 20, 1997, pp. 85-92. ( Preprint )

• Christian Kanzow, Nobuo Yamashita and Masao Fukushima: New NCP-functions and their properties. Journal of Optimization Theory and Applications 94, 1997, pp. 115-135.

• 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.

• 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 )

• 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.

• Andreas Fischer and Christian Kanzow: On finite termination of an iterative method for linear complementarity problems. Mathematical Programming 74, 1996, pp. 279-292. ( Preprint )

• Christian Kanzow: Some noninterior continuation methods for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications 17, 1996, pp. 851-868.

• 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.

• Carl Geiger and Christian Kanzow: On the resolution of monotone complementarity problems. Computational Optimization and Applications 5, 1996, pp. 155-173. ( Preprint )

• Christian Kanzow: Global convergence properties of some iterative methods for linear complementarity problems. SIAM Journal on Optimization 6, 1996, pp. 326-341.

• Christian Kanzow: Nonlinear complementarity as unconstrained optimization. Journal of Optimization Theory and Applications 88, 1996, pp. 139-155.

• 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.

• Christian Kanzow: An unconstrained optimization technique for large-scale linearly constrained convex minimization problems. Computing 53, 1994, pp. 101-117.

• Christian Kanzow: Some equation-based methods for the nonlinear complementarity problem. Optimization Methods and Software 3, 1994, pp. 327-340.

Articles in Refereed Proceedings

• 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.

Preprints

• Christian Kanzow: Newton-type methods for nonlinearly constrained optimization. Preprint 62, Institute of Applied Mathematics, University of Hamburg, Hamburg, December 1992.

• Michael C. Ferris, Christian Kanzow and Todd S. Munson: Feasible descent algorithms for mixed complementarity problems: Complete numerical results. Mathematical Programming Technical Report 98-04-results, Computer Sciences Department, University of Wisconsin - Madison, Madison, WI, March 1998.

• Francisco Facchinei, Andreas Fischer and Christian Kanzow: On the identification of zero variables in an interior-point framework: Complete numerical results. Mathematical Programming Technical Report 98-06-results, Computer Sciences Department, University of Wisconsin - Madison, Madison, WI, May 1998.

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 Komplementaritaetsprobleme. 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.