A neurodynamic algorithm for dependent joint chance constrained geometric programs
This research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transfor...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Results in Control and Optimization |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720723000772 |
| _version_ | 1797754810773012480 |
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| author | Siham Tassouli Abdel Lisser |
| author_facet | Siham Tassouli Abdel Lisser |
| author_sort | Siham Tassouli |
| collection | DOAJ |
| description | This research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transformation to convert the chance-constrained geometric program into a deterministic optimization problem. Then we solve the resulting deterministic program using a dynamical neural network. The stability and convergence of the proposed neural network approach are demonstrated. The primary characteristic of our framework is its ability to solve the dependent joint chance constrained geometric programs without resorting to any convex approximation methods. This feature sets our approach apart from the current state-of-the-art solving techniques. The neurodynamic algorithm is finally applied to solve three geometric optimization problems. |
| first_indexed | 2024-03-12T17:38:47Z |
| format | Article |
| id | doaj.art-84250821afc04e07be9cd6a1918136a2 |
| institution | Directory Open Access Journal |
| issn | 2666-7207 |
| language | English |
| last_indexed | 2024-03-12T17:38:47Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj.art-84250821afc04e07be9cd6a1918136a22023-08-04T05:51:15ZengElsevierResults in Control and Optimization2666-72072023-09-0112100275A neurodynamic algorithm for dependent joint chance constrained geometric programsSiham Tassouli0Abdel Lisser1Corresponding author.; Université Paris Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes (L2S), 3, rue Joliot Curie, 91192 Gif sur Yvette Cedex, FranceUniversité Paris Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes (L2S), 3, rue Joliot Curie, 91192 Gif sur Yvette Cedex, FranceThis research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transformation to convert the chance-constrained geometric program into a deterministic optimization problem. Then we solve the resulting deterministic program using a dynamical neural network. The stability and convergence of the proposed neural network approach are demonstrated. The primary characteristic of our framework is its ability to solve the dependent joint chance constrained geometric programs without resorting to any convex approximation methods. This feature sets our approach apart from the current state-of-the-art solving techniques. The neurodynamic algorithm is finally applied to solve three geometric optimization problems.http://www.sciencedirect.com/science/article/pii/S2666720723000772Copula theoryBiconvex optimizationDynamical neural networkPartial KKT systemChance constrained geometric programs |
| spellingShingle | Siham Tassouli Abdel Lisser A neurodynamic algorithm for dependent joint chance constrained geometric programs Results in Control and Optimization Copula theory Biconvex optimization Dynamical neural network Partial KKT system Chance constrained geometric programs |
| title | A neurodynamic algorithm for dependent joint chance constrained geometric programs |
| title_full | A neurodynamic algorithm for dependent joint chance constrained geometric programs |
| title_fullStr | A neurodynamic algorithm for dependent joint chance constrained geometric programs |
| title_full_unstemmed | A neurodynamic algorithm for dependent joint chance constrained geometric programs |
| title_short | A neurodynamic algorithm for dependent joint chance constrained geometric programs |
| title_sort | neurodynamic algorithm for dependent joint chance constrained geometric programs |
| topic | Copula theory Biconvex optimization Dynamical neural network Partial KKT system Chance constrained geometric programs |
| url | http://www.sciencedirect.com/science/article/pii/S2666720723000772 |
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