A one-layer recurrent neural network for robust linear programming subject to l_∞ norm uncertainty.

Abstract

Robust optimization problems subject to norm uncertainty appear in numerous applications in various fields such as engineering, logistics, and finance. Despite its importance, robust optimization algorithms face significant computational challenges for solving high-dimensional problems, limiting their practical use. This paper presents a neurodynamic approach to mitigate these challenges by transforming the robust linear programming to a non-smooth convex optimization through parameter elimination. A one-layer projection neural network with proven stability and convergence is proposed to solve the non-smooth optimization problem. The effectiveness of this approach is validated based on simulations of numerical examples and applications in reactor design and wastewater treatment.