Event Type:

Analysis Seminar

Date/Time:

Monday, February 17, 2014 - 04:00

Guest Speaker:

Institution:

Portland State University

Abstract:

Some geometric properties of convex sets and convex functions had been studied before the 1960s by many outstanding mathematicians, first of all by Hermann Minkowski and Werner Fenchel. Motivated by the needs of solving optimization problems with nonsmooth data, at the beginning of the 1960s, a generalized differentiation theory for convex functions and sets was rigorously developed in the works of R. Tyrrell Rockafellar and Jean-Jacques Moreau starting the development of convex analysis. Convex analysis serves as the mathematical foundation for convex optimization, a field with increasing impact on many areas of mathematics, applied sciences, and practical applications. In this talk we present a simple path to access generalized differentiation of convex objects in finite dimensions. A geometric approach is employed to develop basic calculus rules for normal cones to convex sets and subgradients of convex functions that are in the mainstream of convex theory. We also present applications of convex analysis to some problems of convex optimization.