A recurrent neural network for solving a class of generalized convex optimization problems

• Published in: Neural networks Vol. 44; pp. 78 - 86
• Main Authors: Hosseini, Alireza, Wang, Jun, Hosseini, S. Mohammad
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2013; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Differential inclusion; Exact sciences and technology; Generalized convex; Mathematical analysis; Mathematics; Neural Networks (Computer); Nonsmooth optimization; Ordinary differential equations; Problem Solving; Pseudoconvexity; Recurrent neural networks; Sciences and techniques of general use; Time Factors; Recurrent neural networks; Generalized convex; Nonsmooth optimization; Differential inclusion; Pseudoconvexity; Recurrent neural nets; Generalized function; Neural network; Modeling; Convex programming; Constrained optimization; Nonsmooth analysis; Optimal solution; Inequality constraint; Equality constraint; Convex function; Objective function; Regularity; Inequality; Mathematical programming
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/j.neunet.2013.03.010

In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem.