A novel neural network based on NCP function for solving constrained nonconvex optimization problems

• Published in: Complexity (New York, N.Y.) Vol. 21; no. 6; pp. 130 - 141
• Main Authors: Effati, Sohrab, Moghaddas, Mohammad
• Format: Journal Article
• Language: English
• Published: Hoboken John Wiley & Sons, Inc 01.07.2016
• Subjects: Equilibrium; Inequality; Lagrangian function; Liapunov functions; Linear programming; Mathematical programming; NCP function; Neighborhoods; neural network; Neural networks; nonconvex optimization; Optimization; p‐power convexification method; Simulation; stability
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1002/cplx.21673

This article presents a novel neural network (NN) based on NCP function for solving nonconvex nonlinear optimization (NCNO) problem subject to nonlinear inequality constraints. We first apply the p‐power convexification of the Lagrangian function in the NCNO problem. The proposed NN is a gradient model which is constructed by an NCP function and an unconstrained minimization problem. The main feature of this NN is that its equilibrium point coincides with the optimal solution of the original problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed NN is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, simulation results on two numerical examples and two practical examples are given to show the effectiveness and applicability of the proposed NN. © 2015 Wiley Periodicals, Inc. Complexity 21: 130–141, 2016