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4  Summary

COPL_GP (Computational Optimization Program Library: Geometric Programming) is a highly efficient and accurate computer program developed in Computational Optimization Laboratory, Department of Management Science, The University of Iowa, Iowa City, IA 52242, USA (http://dollar.biz.uiowa.edu/col/ye) for solving the classical posynomial geometric programming problems. The approach is by means of a primal–dual algorithm developed simultaneously for (i), the dual geometric program after logarithmic transformation of its objective function and (ii), its Lagrangian dual program. Under rather general assumptions, the mechanism defines a primal–dual infeasible path from a specially constructed, perturbed Karush–Kuhn–Tucker system. Subfeasible solutions, are generated for each program whose primal and dual objective function values converge to the respective primal and dual program values.

The basic technique is one of a predictor–corrector type involving Newton's method applied to the perturbed KKT system, coupled with effective techniques for choosing iterate directions and step lengths. Sophisticated implementation techniques and advanced sparse matrix factorizations are used to take advantage of the very special structure of the Hessian matrix of the logarithmically transformed dual objective function.

Computational results on 19 of the most challenging GP problems found in the literature are encouraging. The performance indicates that the algorithm is effective regardless of the degree of difficulty, which is a generally accepted measure in geometric programming.

Geometric programming GP is a very broad class of mathematical problems which is useful in the study of a variety of optimization problems. Its great impact has been in the areas of (1) engineering design : [8],[2], [11], and [12]; (2) economics & statistics : [5], [17], [4], [13],[1], and [3]; (3) manufacturing: [14], [10],[18], and (4) chemical equilibrium : [8], [2], [16]).

The technical details of COPL_GP can be found in Kortanek, Xu and Ye [15]

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