Classification Schemes for Convex Conjugate Transform Dual Families.

Abstract

By using the Ben Israel-Charnes-Kortanek classification theorem for convex sets, an analogous classification scheme is developed for convex conjugate transform dual families applicable to each of the equivalent problem formulations of Fenchel, Fockafellar, and Peterson, including the bifunctional representation. BCK duality states are introduced for convex conjugate problems, and it is determined which ones are possible and which are not. The classification theorem is valid for any paired real topological vector spaces having the Hahn-Banach extension property when any proper convex bifunction is specified. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1971
Accession Number
AD0736096

Entities

People

  • K. O. Kortanek

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Classification
  • Convex Sets
  • Mathematics
  • Theorems
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra
  • Neural Network Machine Learning.

Technology Areas

  • Space