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Duality for linear multiplicative programs

Published online by Cambridge University Press:  17 February 2009

Carlton H. Scott  and
Thomas R. Jefferson
Carlton H. Scott
Affiliation:
Graduate School of Management, University of California, Irvine, CA 92697-3125, USA; e-mail: chscott@gsm.uci.edu.
Thomas R. Jefferson
Affiliation:
Decision and Information Sciences Department, Warrington School of Business, University of Florida, Gainesville, FL, USA.
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Abstract

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Linear multiplicative programs are an important class of nonconvex optimisation problems that are currently the subject of considerable research as regards the development of computational algorithms. In this paper, we show that mathematical programs of this nature are, in fact, a special case of more general signomial programming, which in turn implies that research on this latter problem may be valuable in analysing and solving linear multiplicative programs. In particular, we use signomial programming duality theory to establish a dual program for a nonconvex linear multiplicative program. An interpretation of the dual variables is given.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 393 - 397
Copyright
Copyright © Australian Mathematical Society 2005

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