Primal-Dual algorithms for Abstract convex functions with respect to quadratic functions

TL;DR

This paper introduces primal-dual algorithms for saddle point problems involving abstract convex functions relative to quadratic functions, providing convergence analysis and numerical validation.

Contribution

It develops primal-dual algorithms tailored for abstract convex functions with respect to quadratic functions, including convergence proofs and practical testing.

Findings

Algorithms converge under certain conditions

Numerical experiments demonstrate effectiveness

Framework extends classical convex optimization methods

Abstract

We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate the convergence under certain restrictions. We test our algorithms by several numerical examples.