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Set-valued Optimization : An Introduction with Applications
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| Abstract | Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between ce...rtain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality, and applications in economics among other things.show more |
| Table of Contents | Introduction Order Relations and Ordering Cones Continuity and Differentiability Tangent Cones and Tangent Sets Nonconvex Separation Theorems Hahn-Banach Type Theorems Hahn-Banach Type Theorems Conjugates and Subdifferentials Duality Existence Results for Minimal Points Ekeland Variational Principle Derivatives and Epiderivatives of Set-valued Maps Optimality Conditions in Set-valued Optimization Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities Numerical Methods for Solving Set-valued Optimization Problems Applications.show more |
| Print Version | https://hdl.handle.net/2324/1001548363 |
| View fulltext | Springer Mathematics and Statistics eBooks 2015 English/International: 2015 |
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| Created Date | 2023.09.29 |
| Modified Date | 2024.01.30 |