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Numerical Mathematics and Optimization

TALK: Patrick Mehlitz (BTU Cottbus–Senftenberg & University of Mannheim)

Second-order sufficient conditions are, in a way, easy
Date: 11/24/2022, 10:30 AM
Location: Hubland Nord, Geb. 30, 30.02.003
Organizer: Lehrstuhl für Mathematik VII

Abstract: In this talk, we readdress the classical topic of second-order sufficient optimality conditions in constrained optimization from the viewpoint of variational analysis. Based on the so-called second subderivative of the indicator function associated with the feasible set, one easily obtains abstract second-order sufficient conditions. This observation motivates to study the calculus associated with the second subderivative of set indicators. Our investigations turn out to yield surprisingly simple image and pre-image rules which do not require validity of constraint qualifications in many popular settings. These findings are illustrated in terms of second-order sufficient optimality conditions for optimization problemswith geometric constraints, including so-called disjunctive programs (like complementarity- or cardinality-constrained problems) as well as nonlinear second-order cone and semidefinite programs which will be discussed in detail.

This talk is based on joint work with Matúš Benko, University of Vienna.