Fixed Point Theory, Variational Analysis, and Optimization
Fixed Point Theory, Variational Analysis, and Optimization

Author: Saleh Abdullah R. Al-Mezel

Publisher: CRC Press

Published: 2014-06-03

Total Pages: 368

ISBN-13: 1482222086

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Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol

Iterative Approximation of Fixed Points
Iterative Approximation of Fixed Points

Author: Vasile Berinde

Publisher: Springer

Published: 2007-04-20

Total Pages: 338

ISBN-13: 3540722343

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This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Hemivariational Inequalities
Hemivariational Inequalities

Author: Panagiotis D. Panagiotopoulos

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 453

ISBN-13: 3642516777

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The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Iterative Methods for Fixed Point Problems in Hilbert Spaces
Iterative Methods for Fixed Point Problems in Hilbert Spaces

Author: Andrzej Cegielski

Publisher: Springer

Published: 2012-09-14

Total Pages: 312

ISBN-13: 3642309011

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Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

Impulse Control and Quasi-variational Inequalities
Impulse Control and Quasi-variational Inequalities

Author: Alain Bensoussan

Publisher: Bordas Editions

Published: 1984

Total Pages: 712

ISBN-13:

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"The general aim of this book is to establish and study the relations that exist, via dynamic programming, between, on the one hand, stochastic control, and on the other hand variational and quasi-variational inequalities, with the intention of obtaining constructive methods of solution by numerical methods. It begins with numerous examples which occur in applications and goes on to study, from an analytical viewpoint, both elliptic and parabolic quasi-variational inequalities. Finally the authors reconstruct an optimal control starting from the solution of the quasi-variational inequality."--Amazon.

Uncertainty Quantification in Variational Inequalities
Uncertainty Quantification in Variational Inequalities

Author: Joachim Gwinner

Publisher: CRC Press

Published: 2021-12-21

Total Pages: 334

ISBN-13: 1351857665

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Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature