A. Berkelaar, C. Dert, B. Oldenkamp and S. Zhang, A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming, EI Report 9918/A, EUR. Home/Search Document Details and Download
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Tree-Sparse Convex Programs - Steinbach (2001) (Correct)
....The theoretical analysis leads to natural solution algorithms which combine a dynamic recursion with local projections for local constraints and a Schur complement approach for global constraints, giving linear complexity in the tree size. Other interior approaches for stochastic programs include [2, 6, 9, 11, 13, 20, 23] (twostage LP case) and [5, 12, 19, 27] linear or convex multistage case) We compare our framework with these approaches and with the generalized linear quadratic control formulations developed by Rockafellar [24, 25] and Rockafellar and Wets [26] The material is organized as follows. After ....
....= f0g [ S(0) f0g [ L; b) the objective is linear; c) all constraints are formulated as dynamics or nonnegativity constraints. Under the full rank condition (A1.2 impl ) on P j , assumptions (A1.1 impl ) A2 impl ) will hold. Several interior methods have been developed for this problem class [2, 6, 9, 11, 13, 20, 23]; most of them turn out to be encompassed within our framework. TREE SPARSE CONVEX PROGRAMS 17 TABLE 1. Corresponding matrix blocks in Birge and Holmes [9, x3.4] and Steinbach [32, x4.2] index 2 indicates blocks after projection) given generated [9] A 0 W l T l D 2 0 A 0 A 0 D 2 l S ....
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A. BERKELAAR, C. DERT, B. OLDENKAMP, AND S. ZHANG, A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming, EI-Report 9918, Econometric Institute, Erasmus University, Rotterdam, The Netherlands, Mar. 1999.
A Primal-Dual Decomposition Algorithm for Multistage.. - Berkelaar.. (2000) Self-citation (Berkelaar Zhang) (Correct)
....In fact, our computational approach relies on the homogeneous self dual method originally introduced by Xu, Hung and Ye [28] as a simplification of the self dual embedding technique of Ye, Todd and Mizuno [30] for linear programming. This method was applied by Berkelaar, Dert, Oldenkamp, and Zhang [4] for solving two stage stochastic linear programming problems. The crucial observation made by Berkelaar, Dert, Oldenkamp, and Zhang in [4] is that it is possible to completely decompose the direction finding problem into subproblems, therefore enabling a decomposition based implementation of the ....
....of the self dual embedding technique of Ye, Todd and Mizuno [30] for linear programming. This method was applied by Berkelaar, Dert, Oldenkamp, and Zhang [4] for solving two stage stochastic linear programming problems. The crucial observation made by Berkelaar, Dert, Oldenkamp, and Zhang in [4] is that it is possible to completely decompose the direction finding problem into subproblems, therefore enabling a decomposition based implementation of the HSD technique. The aim here is to show that this result also holds for multistage problems with general convex objective functions as ....
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A. Berkelaar, C. Dert, B. Oldenkamp, and S. Zhang, A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming, Report 9918/A, Econometric Institute, Erasmus University Rotterdam, 1999. (Revision submitted to Operations Research).
A Primal-Dual Interior Point and Decomposition Approach to.. - Zhang (2001) Self-citation (Zhang) (Correct)
....nature of multiple stage stochastic programming. In this paper we shall introduce a particular method of this type, using the so called homogeneous self dual embedding technique and the central path following method. The results presented in this 3 paper are based on the author s earlier papers, [2] and [3] and are made simpler for the expository purpose. In [3] a convex objective function is allowed. 2 Two stage stochastic linear programming Before we talk about the solution methods, let us first consider the models. We start with two stage stochastic linear programming. Two stage ....
....s , x f , x p , x c ) # s.t. 1) 3) 5) and (6) where w 1 and w 2 (w 2 w 1 ) are weights for the first and second stage expected values. Problems of this nature exist widely in the world of finance. In fact, the above described model is taken from Berkelaar, Dert, Oldenkamp and Zhang [2]; two of the authors work for the ABN AMRO Bank, which actually manages similar financial products based on the above model. 7 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 w t=0 t=2 t=1 t=3 Figure 1: Scenario Tree 4 Multiple stage stochastic programming There is of course no need to restrict ourselves to ....
A. Berkelaar, C. Dert, C. Oldenkamp, and S. Zhang, A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming, Report 9918/A, Econometric Institute, Erasmus University Rotterdam, 1999. (To appear in Operations Research).
On implementation of a Lagrangian dual method for - Solving Multi-Stage Stochastic (Correct)
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A. Berkelaar, C. Dert, B. Oldenkamp and S. Zhang, A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming, EI Report 9918/A, EUR.
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