Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Ansari, Qamrul Hasan; Lalitha, C. S.; Mehta, Monika

ISBN 10: 1439868204 ISBN 13: 9781439868201

Published by Chapman and Hall/CRC, 2013

Language: English

Condition: New Hardcover

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Bibliographic Details

Title

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Publisher

Chapman and Hall/CRC

Publication Date

2013

Language

English

ISBN 10

1439868204

ISBN 13

9781439868201

Binding

Hardcover

Condition

New

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Synopsis

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.

The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential.

The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential.

Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

About the Author

Qamrul Hasan Ansari, C. S. Lalitha, Monika Mehta

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