Invexity and Optimization (eBook)

Shashi K. Mishra, Giorgio Giorgi (Autoren)

eBook Download: PDF

2008
X, 266 Seiten
Springer Berlin (Verlag)
978-3-540-78562-0 (ISBN)

Infos

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

Inhalt

Preface 7
Contents 9
1 Introduction 11
2 Invex Functions (The Smooth Case) 21
2.1 Introduction 21
2.2 Invex Functions: De.nitions and Properties 22
2.3 Restricted Invexity and Pointwise Invexity 30
2.4 Invexity and Other Generalizations of Convexity 32
2.5 Domain and Range Transformations: The Hanson – Mond Functions 39
2.6 On the Continuity of the Kernel Function 43
3.-Pseudolinearity: Invexity and GeneralizedMonotonicity 49
3.1 .-Pseudolinearity 49
3.2 Invexity and Generalized Monotonicity 52
4 Extensions of Invexity to Nondi.erentiable Functions 61
4.1 Preinvex Functions 61
4.2 Lipschitz Invex Functions and Other Types of Nonsmooth Invex Functions 70
5 Invexity in Nonlinear Programming 83
5.1 Invexity in Necessary and Su.cient Optimality Conditions 83
5.2 A Su.cient Condition for Invexity Through the Use of the Linear Programming 94
5.3 Characterization of Solution Sets of a Pseudolinear Problem 97
5.4 Duality 99
5.5 Second and Higher Order Duality 110
5.6 Saddle Points, Optimality and Duality with Nonsmooth Invex Functions 113
6 Invex Functions in Multiobjective Programming 125
6.1 Introduction 125
6.2 Kuhn–Tucker Type Optimality Conditions 127
6.3 Duality in Vector Optimization 138
6.4 Invexity in Nonsmooth Vector Optimization 144
6.5 Nonsmooth Vector Optimization in Abstract Spaces 151
6.6 Vector Saddle Points 158
6.7 Linearization of Nonlinear Multiobjective Programming 161
6.8 Multiobjective Symmetric Duality 163
7 Variational and Control Problems Involving Invexity 167
7.1 Scalar Variational Problems with Invexity 167
7.2 Multiobjective Variational Problems with Invexity 178
7.3 Scalar Control Problems 205
7.4 Multiobjective Control Problems 212
8 Invexity for Some Special Functions and Problems 219
8.1 Invexity of Quadratic Functions 219
8.2 Invexity in Fractional Functions and Fractional Programming Problems 223
8.3 Invexity in a Class of Nondi.erentiable Problems 227
8.4 Nondi.erentiable Symmetric Duality and Invexity 247
References 261
Index 275

Produkt-Details

• Erscheint lt. Verlag: 24.4.2008
• Reihe/Serie: Nonconvex Optimization and Its Applications
• Reihe/Serie: Nonconvex Optimization and Its Applications
• Zusatzinfo: X, 266 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: Duality • Generalized convexity • Generalized Monotonicity • Invex Functions • linear optimization • Nonlinear Mathematical Programming • Nonlinear Optimization • Optimality • Optimality conditions • Optimization • Vector Optimization
• ISBN-10: 3-540-78562-0 / 3540785620
• ISBN-13: 978-3-540-78562-0 / 9783540785620