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A global interior point method for nonconvex geometric programming

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Abstract

The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of difference of convex functions. We have developed the necessary and sufficient conditions for global solutions in this standard form. The main challenge in the standard form arises from a constraint of the form \(g(t) \ge 1\), where g is a convex function. We utilize the classical inequality between the weighted arithmetic and harmonic means to overcome this challenge. This enables us to express the optimality conditions as a convex geometric programming problem and employ a predictor-corrector primal-dual interior point method for its solution, with weights updated during the predictor phase. The interior point method solves the dual problem of geometric programming and obtains the primal solution through exponential transformation. We have implemented the algorithm in Fortran 90 and validated it using a set of test problems from the literature. The proposed method successfully solved all the test problems, and the computational results are presented alongside the tested problems and the corresponding solutions found.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their willingness to evaluate this work and for providing valuable feedback, corrections, and suggestions. Their expertise and careful evaluation have significantly contributed to improving this manuscript. This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11081-023-09815-x. Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/acceptedmanuscript-terms.

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Authors and Affiliations

  1. Department of Scientific Computers, Universidade Federal da Paraíba, João Pessoa, Brazil

    Roberto Quirino do Nascimento

  2. Department of Mathematics, Universidade Federal do Mato Grosso do Sul, Campo Grande, Brazil

    Rubia Mara de Oliveira Santos

  3. Coppe Sistemas, Universidade Federal do Rio de janeiro, Rio de Janeiro, Brazil

    Nelson Maculan

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  1. Roberto Quirino do Nascimento
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  2. Rubia Mara de Oliveira Santos
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  3. Nelson Maculan
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Correspondence to Roberto Quirino do Nascimento.

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do Nascimento, R.Q., de Oliveira Santos, R.M. & Maculan, N. A global interior point method for nonconvex geometric programming. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09815-x

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