A global interior point method for nonconvex geometric programming

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 challen...

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Bibliographic Details
Published in:Optimization and engineering 2024-06, Vol.25 (2), p.605-635
Main Authors: do Nascimento, Roberto Quirino, de Oliveira Santos, Rubia Mara, Maculan, Nelson
Format: Article
Language:English
Subjects:
Algorithms
Control
Engineering
Environmental Management
Financial Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Predictor-corrector methods
Research Article
Systems Theory
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Summary: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 ) ≥ 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.
ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-023-09815-x