Variational Sufficiency and Solution Stability in Optimization

TL;DR

This paper explores the relationship between variational stability and strong variational sufficiency, providing fundamental results that enhance understanding of solution robustness and optimality in parameter-shifted optimization problems.

Contribution

It establishes new theoretical links between variational stability and strong variational sufficiency, advancing the understanding of solution behavior under parameter changes.

Findings

Variational stability relates to strong variational sufficiency.

Fundamental results connect stability with local optimality conditions.

Insights improve confidence in optimization model robustness.

Abstract

Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for confidence of outcomes in the design of solution algorithms. Fundamental results are presented here about how such stability relates to a recently developed sufficient condition for local optimality called strong variational sufficiency.