A primal-dual decomposition algorithm for multistage stochastic convex programming

• 成果类型: Article
• 署名作者: Berkelaar, A; Gromicho, JAS; Kouwenberg, R; Zhang, SZ
• 署名单位: Vrije Universiteit Amsterdam; Chinese University of Hong Kong
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0575-6
• 发表日期: 2005
• 页码: 153-177
• 关键词: linear-programs

摘要

This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.