Variational Analysis and Generalized Differentiation: New Trends and Developments
 
 
Description:  Nonsmooth functions, sets with nonsmooth boundaries, and set-valued mappings naturally and frequently appear in various aspects of analysis. Constrained optimization, calculus of variations and its modern form of optimal control, stochastic and statistical problems, mathematical economics, etc., are among those areas of mathematics and its applications, where appropriate tools of generalized differentiation lead to essential achievements. New constructions of generalized differentiations have been recently developed in the framework of the so-called variational analysis, which has been recognized as a fruitful area in mathematics that, on one hand, concerns with the study of optimization-related problems and, on the other hand, applies variational methods to a broad spectrum of non-variational problems. Nonlinear systems and variational principles in physics, economics, and other applied sciences give rise to nonsmooth structures, and these are some of the prime motivations for the development of new forms of analysis. This talk provides an overview of the basic principles, new trends and developments on the generalized differentiation theory with its various applications. The speaker will briefly discuss the contents of his new 2-volume book ???Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications,??? Grundlehren Series (Fundamental Principles of Mathematical Sciences), Vol. 330 and 331, Springer, 2006.
Area(s):
Start Date:  2006-07-05
Start Time:   15:00
Speaker:  Boris Mordukhovich
(Dep. Mathematics, Wayne State Univ.)
Place:  Sala 2.4 - Departamento de Matemática
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