Information Theoretic Approach to Geometric Programming
Abstract
This note shows how information theoretic methods can be used to obtain simply the fundamental geometric inequality lemma. This lemma is the base used by Duffin, Peterson and Zener (1967) for providing their duality results for geometric programming, and its proof occupies three pages in their book. Their method of proof is a technically impressive procedure. However to illustrate the power of information theoretic methods we shall give a simple proof of this fundamental inequality. The approach we shall take is to show the connection between geometric programming and constrained Khinchine-Kullback- Leibler, or minimum discrimination information (MDI) estimation. Complete duality states for MDI estimation are known (c.f. Brockett, Charnes and Cooper (1980), Charnes, Cooper and Seiford (1978), Charnes and Cooper (1974a,b)). Additionally, in the usual duality state of interest, the statistical properties of the solution are known, facilitating sensitivity analysis. The computation of MDI estimation is easily performed using an unconstrained dual convex program involving only linear and exponential functions.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1990
- Accession Number
- ADA227433
Entities
People
- Abraham Charnes
- P. Brockett
Organizations
- University of Texas at Austin