Nonsmooth optimization and semi-algebraic sets

Abstract

Concrete optimization problems, while often nonsmooth, are not pathologically so.
The class of "semi-algebraic" sets and functions - those arising from polynomial
inequalities - nicely exemplifies nonsmoothness in practice. Semi-algebraic sets
(and their generalizations) are common, easy to recognize, and richly structured,
supporting powerful variational properties. In particular I will discuss a generic
property of such sets - partial smoothness - and its relationship with a proximal
algorithm for nonsmooth composite minimization, a versatile model for practical
optimization.

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