Patrick Mehlitz - Asymptotic stationarity and regularity for nonsmooth optimization problems

jnsao:6575 - Journal of Nonsmooth Analysis and Optimization, December 15, 2020, Volume 1 -
Asymptotic stationarity and regularity for nonsmooth optimization problems

Authors: Patrick Mehlitz

Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this new sense are already Mordukhovich-stationary, the presence of a constraint qualification which we call AM-regularity is necessary. We investigate the relationship between AM-regularity and other constraint qualifications from nonsmooth optimization like metric (sub-)regularity of the underlying feasibility mapping. Our findings are applied to optimization problems with geometric and, particularly, disjunctive constraints. This way, it is shown that AM-regularity recovers recently introduced cone-continuity-type constraint qualifications, sometimes referred to as AKKT-regularity, from standard nonlinear and complementarity-constrained optimization. Finally, we discuss some consequences of AM-regularity for the limiting variational calculus.

Volume: Volume 1
Section: Original research articles
Published on: December 15, 2020
Accepted on: December 10, 2020
Submitted on: June 18, 2020
Keywords: Mathematics - Optimization and Control,49J52, 49J53, 90C30, 90C33


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