Theory of Multiobjective Optimization (Mathematics in Science and Engineering, Vol. 176) (Volume 176)

Cover
Theory of Multiobjective Optimization
Copyright Page
Contents
Preface
Notation and Symbols
CHAPTER 1 INTRODUCTION
CHAPTER 2 MATHEMATICAL PRELIMINARIES
	2.1 Elements of Convex Analysis
	2.2 Point-To-Set Maps
	2.3 Preference Orders and Domination Structures
CHAPTER 3 SOLUTION CONCEPTS AND SOME PROPERTIES OF SOLUTIONS
	3.1 Solution Concepts
	3.2 Existence and External Stability of Efficient Solutions
	3.3 Connectedness of Efficient Sets
	3.4 Characterization of Efficiencyand Proper Efficiency
	3.5 Kuhn–Tucker Conditions for Multiobjective Programming
CHAPTER 4 STABILITY
	4.1 Families of Multiobjective Optimization Problems
	4.2 Stability for Perturbation of the Sets of Feasible Solutions
	4.3 Stability for Perturbation of the Domination Structure
	4.4 Stability in the Decision Space
	4.5 Stability of Properly Efficient Solutions
CHAPTER 5 LAGRANGE DUALITY
	5.1 Linear Cases
	5.2 Duality in Nonlinear Multiobjective Optimization
	5.3 Geometric Consideration of Duality
CHAPTER 6 CONJUGATE DUALITY
	6.1 Conjugate Duality Based on Efficiency
	6.2 Conjugate Duality Based on Weak Efficiency
	6.3 Conjugate Duality Based on Strong Supremum and Infimum
CHAPTER 7 METHODOLOGY
	7.1 Utility and Value Theory
	7.2 Stochastic Dominance
	7.3 Multiobjective Programming Methods
References
Index