Abstract
This paper considers a nonconvex geometric optimization problem with two-sided joint probabilistic 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 corresponding 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 illustrate the performances of our approach, we conducted several tests on a minimum transport cost problem and a shape optimization problem.
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Tassouli, S., Lisser, A. A neurodynamic approach for joint chance constrained rectangular geometric optimization. Optim Lett (2023). https://doi.org/10.1007/s11590-023-02050-4
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DOI: https://doi.org/10.1007/s11590-023-02050-4