Second-Order Parametric Free Dualities for Complex Minimax Fractional Programming

Tone-Yau Huang

doi:10.3390/math8010067

Abstract

In this paper, we will consider a minimax fractional programming in complex spaces. Since a duality model in a programming problem plays an important role, we will establish the second-order Mond–Weir type and Wolfe type dual models, and derive the weak, strong, and strictly converse duality theorems.

Highlights

The minimax theorems are very important results in fixed point theory, game theory, minimax programming problems, etc
John Nash provided an alternative proof of the minimax theorem using
Many authors considered the left-hand side of the above equality with some constraints, as a minimax programming problem

Summary

Introduction

The minimax theorems are very important results in fixed point theory, game theory, minimax programming problems, etc. Authors considered various types of the complex minimax programming problems, established the optimality conditions, and studied various types of duality models under some generalized convexities (see [14,15,16,17,18]). Huang and Lai [20] established the second-order parametric duality for complex minimax fractional programming problem, and derived the duality theorems under generalized Θ-bonvexity. Our main goals of this paper will establish two types of second-order parametric free dual model for the complex minimax fractional programming problem (P), and prove that the weak, strong, and strictly converse duality theorems under generalized Θ-bonvexity assumptions.

Preliminary

Second-Order Mond–Weir Type Dual Model

Second-Order Wolfe Type Dual Model

Conclusions and Further Plausible