IJPAM: Volume 56, No. 4 (2009)

A NEW DUALITY FOR
SEMIDEFINITE MULTIPLICATIVE PROGRAMMING

Kai Jie Zheng$^1$Institute for Information and System Science; Xi'an Jiaotong University; Xi'an, 710049, P.R. CHINA, Ji Gen Peng$^2$, Sheng Gui Zhang$^3$
$^{1,2}$Institute for Information and System Science
Xi'an Jiaotong University
Xi'an, 710049, P.R. CHINA
$^1$e-mails: kaijiezheng@gmail.com, kj065@sina.com
$^2$e-mail: jgpeng@mail.xjtu.edu.cn
$^{1,3}$School of Mathematics and Computer Science
Fujian Normal University
Fuzhou, 350007, P.R. CHINA
e-mail: zsgll@fjnu.edu.cn


Abstract.Multiplicative programs are a difficult class of nonconvex programs that have received increasing attention because of their various applications. However, due to the nonconvex nature, few theoretical results are available. In this paper, we show that the semidefinte multiplicative programming is a special geometric programming. Using the results from the classical geometric programming, a new duality is obtained. The duality programming is convex programming. Meantime, the optimal conditions are also obtained.

Received: September 18, 2008

AMS Subject Classification: 46N10

Key Words and Phrases: semidefinite programming, multiplicative programming, geometry duality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 4