A neurodynamic approach to solve rectangular programs with joint probabilistic constraints
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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