Stability 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
