Theory of multiobjective optimization / Yoshikazu Sawaragi, Hirotaka Nakayama, Tetsuzo Tanino
- Mathematics in science and engineering, v. 176
- Front 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 Problems4.2 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 METHODOLOGY7.1 Utility and Value Theory; 7.2 Stochastic Dominance; 7.3 Multiobjective Programming Methods; References; Index.
- In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank.
- 9780080958668 (electronic bk.)
0080958664 (electronic bk.)
- Bibliography Note:
- Includes bibliographical references (pages 281-291) and index.
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