Study of Variable Ordering Structure

Abstract

The work being presented in the present thesis is devoted to the study of Variable Ordering Structure. The chapterwise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes solution concept of vector optimization problem and set optimization problem, various examples have been discussed to elaborate these concepts. This chapter also introduces variable ordering structure. In Chapter 2, we have studied the solution concept of vector optimization problem with variable ordering structure. The aim of this chapter is to present various basic and important results of vector optimization problem with variable ordering structure. In Chapter 3, we have taken the idea of variable ordering structure to set optimization problem. And we collect several optimality notions based on the two binary relations introduced in Chapter 1. We compare these new concepts with known concepts in partially ordered spaces. 2