Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 970723, 16 pages
doi:10.1155/2009/970723
Research Article

Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem

Zhong Wan,1 ShaoJun Zhang,1 and YaLin Wang2

1School of Mathematics Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, China
2School of Information Sciences and Engineering, Central South University, Changsha, Hunan 410083, China

Received 17 December 2008; Revised 18 April 2009; Accepted 7 July 2009

Academic Editor: Kok Teo

Copyright © 2009 Zhong Wan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new approach was proposed to reformulate the biobjectives optimization model of portfolio management into an unconstrained minimization problem, where the objective function is a piecewise quadratic polynomial. We presented some properties of such an objective function. Then, a class of penalty algorithms based on the well-known conjugate gradient methods was developed to find the solution of portfolio management problem. By implementing the proposed algorithm to solve the real problems from the stock market in China, it was shown that this algorithm is promising.