This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.
Author(s): Shashi Kant Mishra, Shouyang Wang, Kin Keung Lai
Edition: 1
Year: 2007
Language: English
Pages: 170
Contents......Page 8
1.1 Introduction......Page 10
1.2 Multiobjective Programming Problems......Page 11
1.3 V – Invexity......Page 12
1.4 Efficient Solution for Optimal Problems with Multicriteria......Page 18
2.1 Introduction......Page 22
2.2 Sufficiency of the Kuhn-Tucker Conditions......Page 24
2.3 Necessary and Sufficient Optimality Conditions for a Class of Nondifferentiable Multiobjective Programs......Page 26
2.4 Duality......Page 30
2.5 Duality for a Class of Nondifferentiable Multiobjective Programming......Page 36
2.6 Vector Valued Infinite Game and Multiobjective Programming......Page 42
3.1 Introduction......Page 47
3.2 Necessary and Sufficient Conditions for Optimality......Page 49
3.3 Duality in Multiobjective Fractional Programming......Page 54
3.4 Generalized Fractional Programming......Page 60
3.5 Duality for Generalized Fractional Programming......Page 65
4.1 Introduction......Page 70
4.2 V-Invexity of a Lipshitz Function......Page 71
4.3 Sufficiency of the Subgradient Kuhn-Tucker Conditions......Page 75
4.4 Subgradient Duality......Page 81
4.5 Lagrange Multipliers and Saddle Point Analysis......Page 90
5.1 Introduction......Page 96
5.2 Necessary Optimality Conditions......Page 98
5.3 Sufficent Optimality Conditions for Composite Programs......Page 100
5.4 Subgradient Duality for Composite Multiobjective Programs......Page 107
5.5 Lagrange Multipliers and Saddle Point Analysis......Page 111
5.6 Scalarizations in Composite Multiobjective Programming......Page 116
6.1 Introduction......Page 119
6.2 V – Invexity for Continuous-time Problems......Page 120
6.3 Necessary and Sufficient Optimality Criteria......Page 125
6.4 Mond-Weir type Duality......Page 128
6.5 Duality for Multiobjective Control Problems......Page 130
6.6 Duality for a Class of Nondifferentiable Multiobjective Variational Problems......Page 142
References......Page 153
P......Page 167
W......Page 168
K......Page 169
Z......Page 170
