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The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and finally presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed; this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.
Nonsmooth optimization. --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Global analysis (Mathematics). --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis
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This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained. This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers.
Variational inequalities (Mathematics) --- Nonsmooth optimization. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Inequalities, Variational (Mathematics) --- Differential inequalities --- Differential equations, partial. --- Mathematics. --- Functional Analysis. --- Partial Differential Equations. --- Applications of Mathematics. --- Math --- Science --- Partial differential equations --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations
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