Overview

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 certain 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 economicsamong other things.

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9783642542640

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This massive and very well-written book will probably be for many years the primary reference in set-valued optimization, the area of optimization where the objective and/or constraint functions of the considered problems are set-valued maps. ... this book will be a solid reference for everyone interested in set-valued optimization, be they graduate students or established scientists. (Sorin-Mihai Grad, zbMATH 1308.49004, 2015)

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