Generic continuity of the perturbed minima of certain parametric optimization problems

TL;DR

This paper demonstrates that in a broad setting, parametric optimization problems can be perturbed to ensure they are well-posed, with applications to Stechkin theory.

Contribution

It introduces a general framework showing how perturbations can make parametric optimization problems well-posed, extending the understanding of solution stability.

Findings

Parameterized problems can be generically well-posed after perturbation

Application to Stechkin theory enhances its scope

Provides conditions for stability of perturbed minima

Abstract

We show that in a quite general framework, the parameterized optimization problem can be so perturbed as to be generically well-posed. As an application, we provide a contribution to Stechkin theory.