Pi-Approximation and Decomposition of Large-Scale Problems

Nurminski, E.A. ORCID: https://orcid.org/0000-0002-7236-6955 (1981). Pi-Approximation and Decomposition of Large-Scale Problems. IIASA Research Report (Reprint). IIASA, Laxenburg, Austria: RR-81-011. Reprinted from Optimization and Optimal Control, pp. 79-88 [1981].

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Abstract

Partial or complete dualization of extremum problems often allows the decomposition of initially large-scale problems into smaller ones with some coordinating program of a moderate size. This idea underlies many known schemes of decomposition and the common difficulty often encountered is the problem of restoring the solution of the primal problem. The main idea of this paper is to present an algorithm for providing an easy way of obtaining the solution of the initial primal problem keeping all advantages of the dual one.

The algorithm described here is based on the particular approximation of the aggregated function representing the decomposed way of solving the extremum problem. This approximation looks like a dual problem and its remarkably simple structure makes it possible to solve a corresponding extremum problem in a few iterations.

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