Minimax and Applications - Paperback
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Minimax and Applications - Advanced Mathematical Optimization
This graduate-level textbook provides comprehensive coverage of minimax theory techniques and principles that play a key role in game theory, optimization, and computational complexity research. Published by Springer as part of the Nonconvex Optimization and Its Applications series, this volume serves as an essential resource for advanced mathematics students and researchers.
Core Mathematical Framework
The text addresses fundamental minimax problems formulated as min max f(x, y) where f(x, y) is a function defined on the product of X and Y spaces. Two critical issues form the foundation of the material: establishing sufficient and necessary conditions for equality minmaxf(x, y) = maxminf(x, y), and determining conditions for variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y).
Key Topics Covered
The textbook explores von Neumann's classical minimax theorem, providing rigorous mathematical proofs and applications. Duality theory in linear and convex quadratic programming receives detailed treatment, interpreting minimax theory through alternative perspectives. The material bridges theoretical foundations with practical applications across multiple mathematical disciplines.
Target Audience and Applications
Designed for graduate students and researchers in applied mathematics, operations research, and discrete mathematics, this text assumes strong background in mathematical analysis and calculus. The principles covered have direct applications in computational complexity theory, game theory optimization problems, and advanced research mathematics.
Publication Details
Available in paperback format, this Springer publication represents current developments in minimax theory research. The text maintains academic rigor while providing clear exposition of complex mathematical concepts, making it suitable for both coursework and independent research.
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ", EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x, y) = maxminf(x, y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Edition
Softcover Repri Edition
Contributor(s)
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Minimax and Applications - Advanced Mathematical Optimization
This graduate-level textbook provides comprehensive coverage of minimax theory techniques and principles that play a key role in game theory, optimization, and computational complexity research. Published by Springer as part of the Nonconvex Optimization and Its Applications series, this volume serves as an essential resource for advanced mathematics students and researchers.
Core Mathematical Framework
The text addresses fundamental minimax problems formulated as min max f(x, y) where f(x, y) is a function defined on the product of X and Y spaces. Two critical issues form the foundation of the material: establishing sufficient and necessary conditions for equality minmaxf(x, y) = maxminf(x, y), and determining conditions for variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y).
Key Topics Covered
The textbook explores von Neumann's classical minimax theorem, providing rigorous mathematical proofs and applications. Duality theory in linear and convex quadratic programming receives detailed treatment, interpreting minimax theory through alternative perspectives. The material bridges theoretical foundations with practical applications across multiple mathematical disciplines.
Target Audience and Applications
Designed for graduate students and researchers in applied mathematics, operations research, and discrete mathematics, this text assumes strong background in mathematical analysis and calculus. The principles covered have direct applications in computational complexity theory, game theory optimization problems, and advanced research mathematics.
Publication Details
Available in paperback format, this Springer publication represents current developments in minimax theory research. The text maintains academic rigor while providing clear exposition of complex mathematical concepts, making it suitable for both coursework and independent research.
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ", EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x, y) = maxminf(x, y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Edition
Softcover Repri Edition
Contributor(s)