On the Aubin property of a class of parameterized variational systems

2017/04/03 by Helmut Gfrerer, Gfrerer, Helmut, Jiří V. Outrata +2
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Control and Dynamics of Mobile Robots #Optimization and Variational Analysis #math.OC #msc:49J53 #msc:90C31 #msc:90C46

paper · pdf · doi:10.48550/arxiv.1704.00536

20 pages, 1 figure

arxiv created 2017/04/03 · arxiv updated 2017/04/04

Abstract

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets and also parameterized generalized equations with conic constraints. The new criterion requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.

Related

• On the Aubin property of solution maps to parameterized variational\n systems with implicit constraints
• Stability analysis for parameterized variational systems with implicit\n constraints
• Second-Order Variational Analysis of Parametric Constraint and Variational Systems
• Coderivatives with respect to a set of the normal cone mappings and their applications
• On new generalized differentials with respect to a set and their applications