Optimization with Multivalued Mappings: Theory, Applications and Algorithms (Springer Optimization and Its Applications, 2)
“Optimization with Multivalued Mappings: Theory, Applications and Algorithms” by Stephan Dempe, published by Springer on July 18, 2006, spans 288 pages and is presented in English. This book delves into nondifferentiable nonconvex optimization, particularly focusing on optimization problems that involve multivalued mappings within constraints or as objective functions. It highlights significant advancements in the field since previous publications, addressing new optimality conditions, applications such as water supply system calibration, and innovative solution algorithms.
Readers will find a structured exploration divided into three parts: the first part examines bilevel programming, the second investigates mathematical programs with equilibrium constraints, and the third focuses on multivalued set-valued optimization. Each section features contributions from experts in their respective fields, providing insights into bilevel programming, mathematical programs with equilibrium constraints, and set-valued optimization problems. This edition serves as a comprehensive resource for those interested in the latest developments and methodologies in linear programming and optimization.
Official synopsis Publisher
In the field of nondifferentiable nonconvex optimization, one of the most intensely investigated areas is that of optimization problems involving multivalued mappings in constraints or as the objective function. This book focuses on the tremendous development in the field that has taken place since the publication of the most recent volumes on the subject. The new topics studied include the formulation of optimality conditions using different kinds of generalized derivatives for set-valued mappings (such as, for example, the coderivative of Mordukhovich), the opening of new applications (e.g., the calibration of water supply systems), or the elaboration of new solution algorithms (e.g., smoothing methods).
The book is divided into three parts. The focus in the first part is on bilevel programming. The chapters in the second part contain investigations of mathematical programs with equilibrium constraints. The third part is on multivalued set-valued optimization. The chapters were written by outstanding experts in the areas of bilevel programming, mathematical programs with equilibrium (or complementarity) constraints (MPEC), and set-valued optimization problems.
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