The Daniel J. Epstein Department of Industrial and Systems Engineering
University of Southern California
Optimization problems with coupled nonsmoothness and nonconvexity are pervasive in statistical learning and many engineering areas. They are very challenging to analyze and solve. In particular, since the computation of their minimizers, both local and global, is generally intractable, one should settle for computable solutions with guaranteed properties and practical significance. In the case when these problems arise from empirical risk minimization in statistical estimation, inferences should be applied to the computed solutions to bridge the gap between statistical analysis and computational results.
This talk gives an overview of several nonsmooth function classes and their connections and sketches an iterative surrogation-based algorithm for the minimization of one particular class of non-Clarke regular composite optimization problems. We will also very briefly touch on the general surrogation approach supplemented by exact penalization to handle challenging constraints.
This talk is based on the monograph titled “Modern Nonconvex Nondifferentiable Optimization” joint with Ying Cui at the University of Minnesota, to be published in mid-November 2021.