Scaled Stability in Variational Problems
A. B. Levy · SIAM Journal on Optimization · 2002
We introduce tools called tolerance functions for the study of a new and practical kind of stability for variational problems on normed vector spaces. Our notion of stability is distinguished by the fact that it explicitly addresses distinctions of scale. To support the stability analysis, we study the continuity and differentiability properties of tolerance functions, paying particular attention to comparisons between tolerance functions and the set-valued mappings that are used to encode variational problems. We end with a discussion of how tolerance functions can be used to analyze the convergence of numerical optimization procedures.