Advances in a nested decomposition algorithm for solving staircase linear programs. Technical report SOL 83-2
A staircase linear program is a linear program in which the variables can be partitioned into a set of time periods, with constraints only between adjacent periods. Staircase LPs usually arise in models of economic or industrial planning over time. This report presents a special technique for solving these LPs, which is classified as a nested decomposition approach. This technique applies the Dantzig-Wolfe decomposition principle to the dual of the LP in a recursive manner. The resulting algorithm solves a sequence of small LPs, one corresponding to each period. After being optimized, a given period passes primal information to the period that follows it and dual information to the period that precedes it. In this way, each period is modified and re-optimized several times, until its optimal solution converges to the optimal solution to the full staircase LP. The primary focus of this report is on two major improvements to this basic technique. The first improvement allows each period to pass much more primal information to the period following it. The second improvement allows each period to pass much more dual information to the period preceding it. Initial computational experience has shown that these improvements accelerate convergence, in that considerably fewer period optimizations have to be performed.
- Research Organization:
- Stanford Univ., CA (USA). Systems Optimization Lab.
- DOE Contract Number:
- AT03-76ER72018
- OSTI ID:
- 6028344
- Report Number(s):
- DOE/ER/72018-T8; ON: DE83011188
- Country of Publication:
- United States
- Language:
- English
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