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An introduction to nonsmooth analysis
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ISBN: 0128008253 0128007311 130618388X 9780128008256 9780128007310 Year: 2014 Publisher: Waltham, MA : Academic Press,

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Abstract

Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.Includes different kinds of sub and super differentials as well as generalized gradientsIncludes also the main tools of the theory, as Sum and Chain Rules or Mean Value theoremsContent is introduced in an elementary way, developing many examples, allowing the r


Periodical
Journal of Nonsmooth Analysis and Optimization
ISSN: 27007448


Book
Nonlinear differential problems with smooth and nonsmooth constraints
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ISBN: 0128133937 0128133864 9780128133934 9780128133866 Year: 2018 Publisher: London

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Methods of dynamic and nonsmooth optimization.
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ISBN: 0898712416 9780898712414 Year: 1989 Volume: 57 Publisher: Philadelphia (Pa.): Society for Industrial and Applied Mathematics


Periodical
Demonstratio Mathematica
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ISSN: 23914661

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Book
Geometric control and nonsmooth analysis
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ISBN: 9812776079 9789812776075 9789812776068 9812776060 Year: 2008 Volume: v. 76 Publisher: Singapore Hackensack, NJ :World Scientific

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The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.


Book
Variational and monotonicity methods in nonsmooth analysis
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ISBN: 3030816710 3030816702 Year: 2021 Publisher: Cham, Switzerland : Birkhäuser,

Optimization and control with applications
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ISBN: 1280263318 9786610263318 0387242554 0387242546 1441937099 Year: 2005 Publisher: New York : Springer Science+Business Media,

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This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.

Nonsmooth Analysis
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ISBN: 3540713336 3540713328 Year: 2007 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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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.

Equilibrium problems : nonsmooth optimization and variational inequality models
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ISBN: 1402001614 0306480263 9781402001611 Year: 2001 Volume: 58 Publisher: Boston, MA : Springer US,

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The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

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