Saddle-point theorems for the generalized cone-convex optimizations of set-valued functions

TL;DR

This paper develops saddle-point theorems for generalized cone-convex set-valued optimization problems in topological linear spaces, extending classical results to more complex set-valued contexts.

Contribution

It introduces new saddle-point theorems and scalarization results for preconvexlike set-valued vector optimization problems in topological linear spaces.

Findings

Fakas-Minkowski alternative theorem established

Scalarization theorem proved for set-valued problems

New vector and scalar saddle-point theorems derived

Abstract

This paper works with preconvexlike set-valued vector optimization problems in topological linear spaces. A Fakas-Minkowski alternative theorem, a scalarization theorem, some vector saddle-point theorems and some scalar saddle point theorem are proved.