The Vector-Valued Maximin

✍ Scribed by V.I. Zhukovskiy and M.E. Salukvadze (Eds.)

• Publisher: Academic Press
• Year: 1994
• Tongue: English
• Leaves: 425
• Series: Mathematics in Science and Engineering 193
• Category: Library

✦ Synopsis

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 guarantees is proposed and their properties examined. According to the authors, this new approach is superior primarily because it has the properties of equivalence and interchangeability - antagonistic players should be able to achieve guaranteed results simultaneously. The approach is tested in a competition problem, as well as a pursuit game with noise. This book should be useful for students, postgraduates and specialists who are investigating the different fields of applied mathematics, control theory, economics and near-by directions of scientific knowledge.

✦ Table of Contents

Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Pages xi-xiii
Vladislav Zhukovskiy, Mindia Salukvadze

Notation
Pages xv-xvi

Abstract
Page xvii

Chapter 1 Quasimotions and Their Properties
Pages 1-48

Chapter 2 Slater Optimality
Pages 49-79

Chapter 3 Pareto Optimality
Pages 81-129

Chapter 4 Geoffrion Optimality
Pages 131-167

Chapter 5 Vector-Valued Saddle Points
Pages 169-236

Chapter 6 Vector-Valued Guarantees
Pages 237-280

Chapter 7 The Competition Problem
Pages 281-333

Chapter 8 A Pursuit Game with Noise
Pages 335-369

Appendix 1: Concepts from Topology
Pages 371-376

Appendix 2: Upper Semicontinuous Multivalent Mappings
Pages 377-378

Appendix 3: Auxiliary Propositions from the Theory of Multicriterial Problems
Pages 379-381

Appendix 4: Vector-Valued Maximins in Static Problems
Pages 383-387

References
Pages 389-395

Author Index
Pages 397-399

Subject Index
Pages 401-404