Generalized Convexity, Nonsmooth Variational Inequalities, and - Nonsmooth Optimizatio

"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"--

Product details

• Authors: Q. H. Ansari, Qamrul Hasan Ansari, Qamrul Hasan (Aligarh Muslim University Ansari, Qamrul Hasan Lalitha Ansari, Qamrul Hasan/ Lalitha Ansari, Ansari Qamrul Hasan, C. S. Lalitha, C. S. (University of Delhi South Campus Lalitha, Lalitha C. S., M. Mehta, Monika Mehta, Monika (Satyawati College Mehta, Mehta Monika
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 18.07.2013
• EAN: 9781439868201
• ISBN: 978-1-4398-6820-1
• No. of pages: 296
• Subjects: Humanities, art, music > Art > Interior design, design; Natural sciences, medicine, IT, technology > Mathematics > Analysis; Social sciences, law, business > Business > Miscellaneous; Product Design, MATHEMATICS / General, MATHEMATICS / Applied, BUSINESS & ECONOMICS / Operations Research, TECHNOLOGY & ENGINEERING / Operations Research, Probability & statistics, Engineering: general, Probability and statistics