TITLE: Semi-algebraic optimization theory

SPEAKER: Adrian lewis

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.

Bio:
Adrian S. Lewis was born in England in 1962. He is a Professor at Cornell University in the School of Operations Research and Industrial Engineering. Following his B.A., M.A., and Ph.D. degrees from Cambridge, and Research Fellowships at Queens' College, Cambridge and Dalhousie University, Canada, he worked in Canada at the University of Waterloo (1989-2001) and Simon Fraser University (2001-2004). He is an Associate Editor of the SIAM Journal on Optimization, Mathematics of Operations Research, and the SIAM/MPS Book Series on Optimization, and is a Co-Editor for Mathematical Programming. He received the 1995 Aisenstadt Prize, from the Canadian Centre de Recherches Mathematiques, the 2003 Lagrange Prize for Continuous Optimization from SIAM and the Mathematical Programming Society, and an Outstanding Paper Award from SIAM in 2005. He co-authored "Convex Analysis and Nonlinear Optimization" with J.M. Borwein.

Lewis' research concerns variational analysis and nonsmooth optimization, with a particular interest in optimization problems involving eigenvalues.