Research Reports from the Department of Operations
Document Type
Report
Publication Date
9-1-1975
Abstract
Duality in a normed linear space X, refers to a relationship between a pair of extremum problems: the primal problem on X and the dual problem on the dual space X*. Given a closed convex cone K defined in terms of a set of continuous linear functionals in X*, the dual extremum problems associated with the primal problem. Necessary and sufficient conditions are established so that the "duality gaps" between pairs of primal-dual problems do not exist, that is, the extremal or the optimal values of the primal and dual problems are equal. These conditions prominently involve the conjugate cone of K and they are also specialized for a Hilbert space. The results are illustrated with examples from function spaces.
Keywords
Operations research, Duality theory (Mathematics), Normed linear spaces, Hilbert space, Mathematical optimization, Function spaces
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 374
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Ubhaya, Vasant A., "Duality in Approximation and Conjugate Cones in Normed Linear Spaces" (1975). Research Reports from the Department of Operations. 165.
https://commons.case.edu/wsom-ops-reports/165