Solving linear programs with joint probabilistic constraints with dependent rows using a dynamical neural network

Abstract

In this paper, we study joint probabilistic constrained linear programs with dependent rows. We take the special case where the dependence between the rows is driven by Gumbel–Hougaard copula. We first transform the problem into a deterministic biconvex optimization problem. Then, we solve the obtained problem using a dynamical neural network based on the partial KKT system. We show the stability and the convergence of the proposed neural network. The main feature of our approach is to solve the joint probabilistic constraints problem without the use of any convex approximations. We finally use a problem of profit maximization to evaluate the performances of our approach.