# New Duality Results for Evenly Convex Optimization Problems

## TL;DR

This paper introduces new duality results for evenly convex optimization problems, providing conditions for strong duality, characterizations of subdifferentials, and saddle-point formulations in a generalized convex analysis framework.

## Contribution

It develops an alternative duality framework for evenly convex problems using generalized conjugation and perturbation theory, extending classical duality results.

## Key findings

- Established sufficient conditions for total duality.
- Derived formulae for c-subdifferentials and biconjugates.
- Characterized total duality via saddle-point theory.

## Abstract

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and $c$-subdifferentials are given. Formulae for the $c$-subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality also by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.