On geometric programming problems having negative degrees of difficulty

Article Abstract:

A simple procedure can be adopted to ensure dual feasibility in geometric programming problems with negative difficulty levels. A constant term is added to the primal objective to gain dual feasibility, with the dual in such programming problems usually considered infeasible. The level of infeasibility could be reduced by identifying an approximate dual solution, although there are shortcomings to this procedure. The restricting behaviour of the primal variables is determined by the dual feasible solution.

Models, Usage, Mathematical optimization

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On subsidiary problems in geometric programming

Article Abstract:

A generalized linear program to solve the primal optimum without the need to determine the subsidiary problems is described. The algorithm is an alternative to the dual-based procedure in solving geometric programming problems. Analysis shows that the linearized form provides information in all posynomials including those with slack constraints. In addition, optimal primal-dual relationships yield information on the multiple optima characterizing the primal under those conditions.

Nonlinear programming

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Investigation of path-following algorithms for signomial geometric programming problems

Article Abstract:

The path-following algorithm that can be used to solve signomial geometric programming (GP) dual problems is found to yield better quality and globally optimal results, given a relaxed stopping criterion for early posynomial GP problems in the sequence. The method can be employed to either the original nonconvex problem or to each of a sequence of convex posynomial GP problems nearly equalling the original problem.

Management-Problem Solving, Analysis, Evaluation, Human resource management, Algorithms, Problem solving

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