Generalized Polyhedral Convex Optimization Problems

TL;DR

This paper systematically studies generalized polyhedral convex optimization problems in locally convex spaces, establishing solution existence, optimality conditions, and duality theorems, including conditions for strong duality.

Contribution

It introduces a comprehensive framework for analyzing generalized polyhedral convex problems, including duality and optimality conditions in locally convex spaces.

Findings

Solution existence theorems established

Necessary and sufficient optimality conditions derived

Strong duality holds under multiple conditions

Abstract

Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions, weak and strong duality theorems. In particular, we show that the dual problem has the same structure as the primal problem, and the strong duality relation holds under three different sets of conditions.