Characterizations of Tilt-Stable Minimizers in Second-Order Cone Programming

TL;DR

This paper provides comprehensive second-order variational analysis characterizations of tilt stability for second-order cone programming problems under the weakest constraint qualification, advancing understanding in nonpolyhedral conic optimization.

Contribution

It develops a new approach using second-order variational analysis to characterize tilt stability in second-order cone programming without strong nondegeneracy assumptions.

Findings

Complete neighborhood and point-based characterizations of tilt stability.

Characterizations hold under the weakest metric subregularity constraint qualification.

Advances understanding of tilt stability in nonpolyhedral conic problems.

Abstract

This paper is devoted to the study of tilt stability of local minimizers, which plays an important role in both theoretical and numerical aspects of optimization. This notion has been comprehensively investigated in the unconstrained framework as well as for problems of nonlinear programming with $C^2$-smooth data. Available results for nonpolyhedral conic programs were obtained only under strong constraint nondegeneracy assumptions. Here we develop an approach of second-order variational analysis, which allows us to establish complete neighborhood and pointbased characterizations of tilt stability for problems of second-order cone programming generated by the nonpolyhedral second-order/Lorentz/ice-cream cone. These characterizations are established under the weakest metric subregularity constraint qualification condition.