Set-valued analysis is an essential tool for the mathematical
formulation of many real-life situations, e.g., equilibrium theory
in mathematical economics. This work offers the first comprehensive
treatment in book form of the fairly new subdiscipline of
enlargements of maximal monotone operators, including several
important new results in the field. In the last decades, with the
development of nonsmooth optimization, effective algorithms have
been developed to solve these kinds of problems, such as nonsmooth
variational inequalities. Several of these methods, such as bundle
methods for variational problems, are fully developed and analyzed
in this book.
The first chapters provide a self-contained review of the basic
notions and fundamental results in set-valued analysis, including
set convergence and continuity of set-valued mappings together with
many important results in infinite-dimensional convex analysis,
leading to the classical fixed point results due to Ekeland,
Caristi and Kakutani. Next, an in-depth introduction to monotone
operators is developed, emphasizing results related to maximality
of subdifferentials and of sums of monotone operators. Building on
this foundational material, the second part of the monograph
contains new results (all of them established during the last
decade) on the concept of enlargements of monotone operators, with
applications to variational inequalities, bundle-type methods,
augmented Lagrangian methods, and proximal point algorithms.
Audience:
This book is addressed to mathematicians, engineers, economists,
and researchers interested in acquiring a solid mathematical
foundation in topics such as point-to-set operators, variational
inequalities, general equilibrium theory, and nonsmooth
optimization, among others. Containing extensive exercises and
examples throughout the text, the first four chapters of the book
can also be used for a one-quarter course in set-valued analysis
and maximal monotone operators for graduate students in pure and
applied mathematics, mathematical economics, operations research
and related areas. The only requisites, besides a minimum level of
mathematical maturity, are some basic results of general topology
and functional analysis.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!