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.

本文考虑具有两侧联合概率约束（即矩形约束）的非凸几何优化问题。我们将随机问题转化为确定性问题。此外，我们使用对数变换结合算术几何平均不等式来获得双凸问题。基于所获得程序的双凸结构和相应的部分KKT系统，我们提出了一种动态神经网络来解决初始矩形问题。我们框架的主要特点是提出一种收敛方法来解决矩形联合机会约束优化问题，而不使用任何凸近似，这与最先进的求解方法不同。为了说明我们方法的性能，