First-and Second-Order Convex Programming Scaling Algorithms Applied to Geometric Programming

Paul R. Gribik; Siming Huang; Kenneth O. Kortanek

doi:10.1007/978-1-4615-3600-0_30

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Book chapter

First-and Second-Order Convex Programming Scaling Algorithms Applied to Geometric Programming

Paul R. Gribik, Siming Huang and Kenneth O. Kortanek

Systems and Management Science by Extremal Methods, pp.491-511

Kluwer Academic Publishers

1992

DOI: 10.1007/978-1-4615-3600-0_30

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Abstract

A change of variables based on matrix column scaling is introduced in a linearly constrained convex program. With the transformation of the objective function gradient, a convex scaling algorithm is developed that returns an optimal solution together with “limiting dual conditions.” An enhancement is provided by using a Cholesky decomposition of the transformed Hessian matrix. A convergence analysis is given for geometric programming, together with numerical experiments on test problems in the literature.

Cholesky Decomposition

Convex Program

Dual Condition

Geometric Programming

Scaling Algorithm

Details

Title: Subtitle: First-and Second-Order Convex Programming Scaling Algorithms Applied to Geometric Programming
Creators: Paul R. Gribik
Siming Huang
Kenneth O. Kortanek
Contributors: Fred Young Phillips (Editor)
John James Rousseau (Editor)
Resource Type: Book chapter
Publication Details: Systems and Management Science by Extremal Methods, pp.491-511
DOI: 10.1007/978-1-4615-3600-0_30
Publisher: Kluwer Academic Publishers; Boston
Language: English
Date published: 1992
Academic Unit: Business Analytics
Record Identifier: 9984963193302771

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