A neurodynamic algorithm for dependent joint chance constrained geometric programs

Abstract

This research studies the use of copula theory to model dependencies in joint probabilistic constrained geometric programs with dependent rows. The row vectors are assumed to follow an elliptical distribution, and their dependencies are modeled through a Gumbel–Hougaard copula. We use a log transformation to convert the chance-constrained geometric program into a deterministic optimization problem. Then we solve the resulting deterministic program using a dynamical neural network. The stability and convergence of the proposed neural network approach are demonstrated. The primary characteristic of our framework is its ability to solve the dependent joint chance constrained geometric programs without resorting to any convex approximation methods. This feature sets our approach apart from the current state-of-the-art solving techniques. The neurodynamic algorithm is finally applied to solve three geometric optimization problems.