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Pré-Publication, Document De Travail Année : 2022

A neurodynamic approach to solve rectangular programs with joint probabilistic constraints

Siham Tassouli
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Abdel Lisser

Résumé

This paper considers a noncovex geometric problem with two-sided joint probabilistic inequalities constraints, namely rectangular constraints. We transform the stochastic problem into a deterministic one. Further, we use a logarithmic transformation combined with the arithmetic-geometric mean inequality to obtain a biconvex problem. Based on the biconvex structure of the obtained program and the correspondent partial KKT system, we propose a dynamical neural network to solve the initial rectangular problem. The main feature of our framework is to propose a converging method to solve rectangular joint chance-constrained optimization problems without the use of any convex approximation unlike the state-of-the-art solving methods. To verify the performances of our approach, we conducted several tests on a minimum transport cost problem and a shape optimization problem.
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Dates et versions

hal-03838582 , version 1 (03-11-2022)

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  • HAL Id : hal-03838582 , version 1

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Siham Tassouli, Abdel Lisser. A neurodynamic approach to solve rectangular programs with joint probabilistic constraints. 2022. ⟨hal-03838582⟩
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