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.
Neta, Beny; Reich, Simeon; Victory, H. Dean, Jr. (2002);An existence and uniqueness theory is developed for the energy dependent, steady state neutron diffusion equation with inhomogeneous oblique boundary conditions im- posed. Also, a convergence theory is developed for the ...
E. Polak; Royset, J.O. (2008);We consider a class of stochastic nonlinear programs for which an approximation to a locally optimal solution is speci_ed in terms of a fractional reduction of the initial cost error. We show that such an approximate ...
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 ...