Strong Metric Subregularity of the optimality mapping and second-order sufficient optimality conditions in extremal problems with constraints

TL;DR

This paper reviews recent results on strong metric subregularity in constrained optimization, linking second-order optimality conditions to stability of solutions and multipliers under data perturbations.

Contribution

It summarizes new sufficient conditions for strong metric subregularity in various constrained optimization problems without proofs.

Findings

Sufficient conditions for SMSR based on second-order optimality conditions

Guarantee of stability of solutions and multipliers under small data changes

Applicability to mathematical programming, calculus of variations, and optimal control

Abstract

This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a set of necessary optimality conditions in three types of constrained optimization problems: mathematical programming, calculus of variations, and optimal control. The conditions are based on second-order sufficient optimality conditions in the corresponding optimization problems and guarantee small changes in the optimal solution and Lagrange multipliers for small changes in the data.