Approximations and Solution Estimates in Optimization
Royset, Johannes O.
MetadataShow full item record
Approximation is central to many optimization problems and the supporting theory pro- vides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing nite- and in nite-dimensional constrained minimization prob- lems as instances of extended real-valued lower semicontinuous functions de ned on a general metric space. Since the Attouch-Wets distance between such functions quanti es epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through estimates of that distance. In par- ticular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with modulus one in this distance. We construct a general class of approximations of extended real-valued lower semicontinuous functions that can be made arbitrarily accurate and that involve only a nite number of parameters under additional assumptions on the underlying metric space.
This paper is in review.
Showing items related by title, author, creator and subject.
Corley, M.S.; Santiago, F.; T. Martinez; Agrawal, B.N. (2011);The Navy is interested in horizontal laser propagation studies in a maritime environment, near the ocean surface, for applications including imaging and high-energy laser propagation. The Naval Postgraduate School (NPS) ...
Hayne, William John (Monterey, California. Naval Postgraduate School, 1972-03);Methods for approximating the system hazard function are developed for systems which have constant component failure rates. The approximations are applicable to systems which are "highly reliable," e.g., all component ...
Franke, Richard H. (Monterey, California. Naval Postgraduate School, 1976); NPS-53Fe76121The subject of linear optimal approximation has received considerable attention in recent years , , , , . The subject of multivariate approximation for scattered data, including optimal approximations, is ...