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130626  eng 
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a 9780387697574

100 
1 

a Burachik, Regina S.

245 
0 
0 
a SetValued Mappings and Enlargements of Monotone Operators
h Elektronische Ressource
c by Regina S. Burachik, Alfredo N. Iusem

250 


a 1st ed. 2008

260 


a New York, NY
b Springer US
c 2008, 2008

300 


a XIV, 294 p. 15 illus
b online resource

505 
0 

a Set Convergence and PointtoSet Mappings  Convex Analysis and Fixed Point Theorems  Maximal Monotone Operators  Enlargements of Monotone Operators  Recent Topics in Proximal Theory

653 


a Functional analysis

653 


a Operations Research, Management Science

653 


a Operations research

653 


a Optimization

653 


a Management science

653 


a Functional Analysis

653 


a Calculus of Variations and Optimization

653 


a Operator theory

653 


a Operator Theory

653 


a Mathematical optimization

653 


a Operations Research and Decision Theory

653 


a Calculus of variations

700 
1 

a Iusem, Alfredo N.
e [author]

041 
0 
7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

490 
0 

a Springer Optimization and Its Applications

028 
5 
0 
a 10.1007/9780387697574

856 
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u https://doi.org/10.1007/9780387697574?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515.7

520 


a Setvalued analysis is an essential tool for the mathematical formulation of many reallife 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.

520 


a The first chapters provide a selfcontained review of the basic notions and fundamental results in setvalued analysis, including set convergence and continuity of setvalued mappings together with many important results in infinitedimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an indepth 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, bundletype methods, augmented Lagrangian methods, and proximal point algorithms.

520 


a Audience This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as pointtoset 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 onequarter course in setvalued 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
