โ Scribed by Salukvadze (editor)
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Front Cover
The Vector-Valued Maximin
Copyright Page
Contents
Preface
Notation
Abstract
Chapter 1. Quasimotions and their Properties
1. Reference Information
2. Piecewise-Continuous Stepwise Quasimotion
3. The Alternative and the Saddle Point
4. Corollaries of the Alternative
Chapter 2. Slater Optimality
1. Slater-Maximal Strategy
2. Sufficient Conditions
3. Structure in the Case of Slater Optimality
Chapter 3. Pareto Optimality
1. Pareto-Optimal Strategy
2. Relations Between the Sets P and S
3. Structure in the Case of Pareto Optimality
4. Sufficient Conditions
5. A Linear Quadratic Multicriterial Problem
6. Comparison to P1-Optimality
Chapter 4. Geoffrion Optimality
1. Geoffrion-Maximal Strategy
2. Necessary and Sufficient Conditions
3. A-optimality
Chapter 5. Vector-Valued Saddle Points
1. Definition
2. Properties of Saddle Points
3. Invariance of Vector-Valued Saddle Points
4. Sufficient Conditions
Chapter 6. Vector-Valued Guarantees
1. Vector-Valued Maximin and Minimax
2. Existence of Vector-Valued Maximins
Chapter 7. The Competition Problem
1. Mathematical Model of Competition
2. A Game With Separable Payoff Function
3.The ZS-Solution in the Competition Problem
4. Model of Competing Research Activities
Chapter 8. A Pursuit Game With Noise
1. Statement of Problem
2. Pursuit of Two Target Points, one of which with Uncertain Location
3. Pursuit of Two Target Points
4. A Three-Criteria1 Pursuit Problem
Appendix 1: Concepts from Topology
Appendix 2: Upper Semicontinuous Multivalent Mappings
Appendix 3: Auxiliary Propositions from the Theory of Multicriterial Problems
Appendix 4: Vector-Valued Maximins in Static Problems
A4.1. Slater Maximin
A4.2. Other Notions of Vector-Valued Maximins
References
Author Index
Subject Index
Mathematics in Science and Engineering
๐ SIMILAR VOLUMES
<span>Text: English, Russian (translation)</span>
<span>The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.<br>A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are descr
This work is devoted to the investigation and solution of differential games with a vector-valued pay-off function. Slater-, Pareto- and Geoffrion-optimal strategies are defined for such a game, and their positive and negative properties are examined. A new class of solutions called vector-valued gu
This work is devoted to the investigation and solution of differential games with a vector-valued pay-off function. Slater-, Pareto- and Geoffrion-optimal strategies are defined for such a game, and their positive and negative properties are examined. A new class of solutions called vector-valued gu