Extremal Principles and Optimization Dualities for Khinchin-Kullback-Leibler Estimation.

Abstract

This paper presents a new extremal approach to deriving dual optimization problems with proper duality inequality which simplifies and generalizes the Fenchel-Rockafellar scheme. Our derivation proceeds in two stages, (1) inequality attainment, (2) decoupling primal and dual variables. The power and convenience of this approach are exhibited through a new, much simpler derivation of the Charnes-Cooper results for Khinchin-Kullback-Leibler statistical estimation (1), the immediate establishment of the C(2) duality for general distributions and its extensions to general linear inequality constraints, plus the development of a new two-person zero-sum game connection.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1976
Accession Number
ADA031398

Entities

People

  • Abraham Charnes
  • L. Seiford
  • William W. Cooper

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computer Programming
  • Convex Programming
  • Convex Sets
  • Data Science
  • Decoupling
  • Discrete Distribution
  • Inequalities
  • Information Science
  • Linear Programming
  • Optimization
  • Real Variables
  • Statistical Analysis
  • Statistical Estimation
  • Statistical Inference
  • Statistics
  • Stochastic Processes
  • Zero-Sum Games

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Operations Research