A decomposition-coordination approach for large-scale optimization
- Auburn Univ., AL (United States)
- Univ. of California, Berkeley, CA (United States)
We outline in this paper a general approach to solving distributed optimization problems of a certain type. We assume there are n processing elements, connected together so that they can share information. We expect that our approach would be particularly useful in large-scale problems, where a centralized approach may not be able to find a solution in an acceptable time, or the problem data may inherently be decentralized. However our approach is applicable to problems of any size, provided they meet the conditions we impose to ensure convergence. First we duplicate some (or all) of the problem variables, so as to decompose the constraints into purely local subsets. This produces an artificial decomposition and an increase in the number of variables. In order to make sure the solutions of the new problem and the original one coincide, we introduce consistency constraints which force all duplicated copies of a variable to be equal at the solution. These equality constraints are the only non-local constraints in the resulting transformed problem. We then apply the Auxiliary Problem Principle (APP) to the problem of finding a saddle-point of the Augmented Lagrangian of the transformed optimization problem. Informally, the APP involves linearizing any non-separable terms in -the Augmented Lagrangian and adding convex/concave terms which can be chosen to be separable. Under conditions stated below, the new problem (after applying the APP) has the same saddle- point as the original problem. We describe an iterative algorithm to find the saddle-point of this new problem. By choosing the APP terms to be decomposable, the central step of this iterative algorithm decomposes into independent parallel minimizations, followed by Lagrange multiplier updates which involve only local information transfers.
- OSTI ID:
- 125472
- Report Number(s):
- CONF-950212--
- Country of Publication:
- United States
- Language:
- English
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