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.
General
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