On the implementation of a log-barrier progressive hedging method for multistage stochastic programs

Authors:
Xinwei Liu;Kim-Chuan Toh;Gongyun Zhao
Affiliations:
Department of Applied Mathematics, Hebei University of Technology, Beichen Campus, Tianjin 300401, China;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 10
Cited 0

MSLiP: a computer code for the multistage stochastic linear programming problem

Mathematical Programming: Series A and B
Scenarios and policy aggregation in optimization under uncertainty

Mathematics of Operations Research
Applying the progressive hedging algorithm to stochastic generalized networks

Annals of Operations Research
Approximate scenario solutions in the progressive hedging algorithm: a numerical study

Annals of Operations Research
Parallel decomposition of multistage stochastic programming problems

Mathematical Programming: Series A and B
On convergence of an augmented Lagrangian decomposition method for sparse convex optimization

Mathematics of Operations Research
A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming

Operations Research
A Decomposition Method Based on SQP for a Class of Multistage Stochastic Nonlinear Programs

SIAM Journal on Optimization
A Lagrangian Dual Method with Self-Concordant Barriers for Multi-Stage Stochastic Convex Programming

Mathematical Programming: Series A and B
Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method

INFORMS Journal on Computing

Quantified Score

Hi-index	7.29

Visualization

Abstract

A progressive hedging method incorporated with self-concordant barrier for solving multistage stochastic programs is proposed recently by Zhao [G. Zhao, A Lagrangian dual method with self-concordant barrier for multistage stochastic convex nonlinear programming, Math. Program. 102 (2005) 1-24]. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smoothes the Lagrangian dual function by self-concordant barrier functions. The convergence and polynomial-time complexity of the method have been established. Although the analysis is done on stochastic convex programming, the method can be applied to the nonconvex situation. We discuss some details on the implementation of this method in this paper, including when to terminate the solution of unconstrained subproblems with special structure and how to perform a line search procedure for a new dual estimate effectively. In particular, the method is used to solve some multistage stochastic nonlinear test problems. The collection of test problems also contains two practical examples from the literature. We report the results of our preliminary numerical experiments. As a comparison, we also solve all test problems by the well-known progressive hedging method.