A Novel Recurrent Neural Network for Solving Nonlinear Optimization Problems With Inequality Constraints

• Published in: IEEE transactions on neural networks Vol. 19; no. 8; pp. 1340 - 1353
• Main Authors: Xia, Youshen, Feng, Gang, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2008; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Application software; Applied sciences; Artificial Intelligence; Computer science; control theory; systems; Computer Simulation; Computer systems and distributed systems. User interface; Connectionism. Neural networks; Constraint optimization; Constraints; Convergence; Design engineering; Exact sciences and technology; Global convergence; Inequalities; Lagrangian functions; Linear matrix inequalities; Linear programming; Models, Theoretical; Neural networks; Neural Networks (Computer); nonconvex programming; Nonlinear Dynamics; nonlinear inequality constraints; Nonlinearity; nonsmooth analysis; Optimization; Pattern Recognition, Automated - methods; Projection; recurrent neural network; Recurrent neural networks; Software; Very large scale integration; Recurrent neural nets; nonlinear inequality constraints; Non convex programming; Global convergence; Lagrangian; recurrent neural network; Lyapunov method; nonconvex programming; Nonlinear problems; Non linear programming; Network management; Neural network; Convex programming; Constrained optimization; nonsmooth analysis; Inequality constraint; Kuhn Tucker method; Hessian matrices; Non convex analysis; Lyapunov function; Mathematical programming
• ISSN: 1045-9227; 1941-0093; 1941-0093
• DOI: 10.1109/TNN.2008.2000273

This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush-Kuhn-Tucker point in the sense of Lyapunov and its output trajectory is globally convergent to a minimum solution. Compared with variety of the existing projection neural networks, including their extensions and modification, for solving such nonlinearly constrained optimization problems, it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point. Simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems.