On second-order optimality conditions for $C^{1,1}$ optimization problems via Lagrangian functions

TL;DR

This paper develops new second-order optimality conditions for $C^{1,1}$-smooth optimization problems with constraints using Mordukhovich subdifferentials, extending existing theoretical results and applying to multiobjective cases.

Contribution

It introduces novel second-order optimality conditions for constrained $C^{1,1}$ problems using limiting subdifferentials, refining prior theoretical frameworks.

Findings

Derived new second-order optimality conditions for constrained $C^{1,1}$ problems.

Extended the conditions to multiobjective optimization scenarios.

Refined and extended existing theoretical results in the literature.

Abstract

This paper focuses on optimality conditions for $C^{1,1}$-smooth optimization problems subject to inequality and equality constraints. By employing the concept of limiting (Mordukhovich) second-order subdifferentials to the Lagrangian function associated with the problem, we derive new second-order optimality conditions for the considered problem. Applications for multiobjective optimization problems are studied as well. These results extend and refine existing results in the literature.