V-INVEX FUNCTIONS AND VECTOR OPTIMIZATION

By CHARLES THOMPSON

CONTENTS CHAPTER 1: GENERAL INTRODUCTION 1 1 INTRODUCTION 1 2 MULTIOBJECTIVE PROGRAMMING PROBLEMS 1 4 EFFICIENT SOLUTION FOR OPTIMAL PROBLEMS WITH MULTICRITERIA 2 1 INTRODUCTION 2 2 SUFFICIENCY OF THE KUHN-TUCKER CONDITIONS 2 3 NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMS PROGRAMMING 2 6 VECTOR VALUED INFINITE GAME AND MULTIOBJECTIVE PROGRAMMING CHAPTER 3: MULTIOBJECTIVE FRACTIONAL PROGRAMMING 3 1 INTRODUCTION 3 2 NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMALITY 3 3 DUALITY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING 3 4 GENERALIZED FRACTIONAL PROGRAMMING 3 5 DUALITY FOR GENERALIZED FRACTIONAL PROGRAMMING CHAPTER 4: MULTIOBJECTIVE NONSMOOTH PROGRAMMING 4 1 INTRODUCTION 4 2 V-INVEXITY OF A LIPSHITZ FUNCTION 4 3 SUFFICIENCY OF THE SUBGRADIENT KUHN-TUCKER CONDITIONS 4 4 SUBGRADIENT DUALITY 4 5 LAGRANGE MULTIPLIERS AND SADDLE POINT ANALYSIS CHAPTER 5: COMPOSITE MULTIOBJECTIVE NONSMOOTH PROGRAMMING 5 1 INTRODUCTION 5 2 NECESSARY OPTIMALITY CONDITIONS 1 3 V ?INVEXITY CHAPTER 2: V-INVEXITY IN NONLINEAR MULTIOBJECTIVE PROGRAMMING 2 4 DUALITY 2 5 DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE 5 3 SUFFICENT OPTIMALITY CONDITIONS FOR COMPOSITE PROGRAMS 5 4 SUBGRADIENT DUALITY FOR COMPOSITE MULTIOBJECTIVE PROGRAMS 5 5 LAGRANGE MULTIPLIERS AND SADDLE POINT ANALYSIS 5 6 SCALARIZATIONS IN COMPOSITE MULTIOBJECTIVE PROGRAMMING CHAPTER 6: CONTINUOUS-TIME PROGRAMMING 6 1 INTRODUCTION 6 3 NECESSARY AND SUFFICIENT OPTIMALITY CRITERIA 6 4 MOND-WEIR TYPE DUALITY 6 5 DUALITY FOR MULTIOBJECTIVE CONTROL PROBLEMS 6 6 DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE VARIATIONAL PROBLEMS REFERENCES 6 2 V ?INVEXITY FOR CONTINUOUS-TIME PROBLEMS