Stability and Error Analysis for Optimization and Generalized Equations

Abstract

The article of record as published may be found at https://doi.org/10.1137/19M1251424Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite-dimensional. We consider nonconvex optimization and generalized equations defined on metric spaces and develop bounds on solution errors using the truncated Hausdorff distance applied to graphs and epigraphs of the underlying set-valued mappings and functions. In the process, we extend the calculus of such distances to cover compositions and other constructions that arise in nonconvex problems. The results are applied to constrained problems with feasible sets that might have empty interiors, solution of KKT systems, and optimality conditions for difference-of-convex functions and composite functions.This work was supported in part by DARPA (Lagrange) under grant HR0011-8- 34187, by the ONR (Science of Autonomy) under grant N0001419WX00183, and by the AFOSR (Optimization and Discrete Mathematics) under grant F4FGA08272G001.This work was supported in part by DARPA (Lagrange) under grant HR0011-8- 34187, by the ONR (Science of Autonomy) under grant N0001419WX00183, and by the AFOSR (Optimization and Discrete Mathematics) under grant F4FGA08272G001