Subdifferential Stability Analysis for Convex Optimization Problems via Multiplier Sets

TL;DR

This paper investigates the stability of convex optimization problems by deriving formulas for subdifferentials of the optimal value function using multiplier sets, enhancing understanding of solution sensitivity.

Contribution

It introduces new formulas for subdifferential and singular subdifferential computation in convex problems through multiplier sets, advancing stability analysis methods.

Findings

Formulas for subdifferential of the optimal value function

Formulas for singular subdifferential of the optimal value function

Application to stability analysis in convex programming

Abstract

This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computing or estimating the subdifferential and the singular subdifferential of the optimal value function via suitable multiplier sets.