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

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Chapman and Hall/CRC
• Seitenzahl: 298
• Erscheinungstermin: 18. Juli 2013
• Englisch
• Abmessung: 240mm x 161mm x 21mm
• Gewicht: 614g
• ISBN-13: 9781439868201
• ISBN-10: 1439868204
• Artikelnr.: 32842077

Autorenporträt

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

Inhaltsangabe

Generalized Convexity and Generalized Monotonicity: Elements of Convex
Analysis. Generalized Derivatives and Generalized Subdifferentials.
Nonsmooth Convexity. Monotonocity and Generalized Monotonicity. Nonsmooth
Variational Inequalities and Nonsmooth Optimization: Elements of
Variational Inequalities. Nonsmooth Variational Inequalities.
Characterizations of Solution Sets of Optimization Problem and Nonsmooth
Variational Inequalities. Nonsmooth Generalized Variational Inequalities
and Optimization Problems. Appendices. Index.