Duality for linear multiplicative programs

ANZIAM J. 46 (2005), 393-397

Duality for linear multiplicative programs

Carlton H. Scott
Graduate School of Management
University of California
Irvine, CA 92697-3125
USA
chscott@gsm.uci.edu

and

Thomas R. Jefferson
Decision and Information Sciences Department
Warrington School of Business
University of Florida
Gainesville FL
USA

Abstract

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.

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