Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints

Extended linear-quadratic programming (ELQP) is an extension of the conventional linear programming and quadratic programming, which arises in many dynamic and stochastic optimization problems. Existing neural network approaches are limited to solve ELQP problems with bound constraints only. In the paper, I consider solving the ELQP problems with general polyhedral sets by using recurrent neural networks. An existing neural network in the literature, called general projection neural network (GPNN) is investigated for this purpose. In addition, based on different types of constraints, different approaches are utilized to lower the dimensions of the designed GPNNs and consequently reduce their structural complexities. All designed GPNNs are stable in the Lyapunov sense and globally convergent to the solutions of the ELQP problems under mild conditions. Numerical simulations are provided to validate the results.

[1]  Xiaolin Hu,et al.  Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network , 2006, IEEE Transactions on Neural Networks.

[2]  L. Liao,et al.  A neural network for a class of convex quadratic minimax problems with constraints , 2004, IEEE Transactions on Neural Networks.

[3]  Jinde Cao,et al.  A delayed neural network for solving linear projection equations and its analysis , 2005, IEEE Transactions on Neural Networks.

[4]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[5]  Jun Wang,et al.  A general projection neural network for solving monotone variational inequalities and related optimization problems , 2004, IEEE Transactions on Neural Networks.

[6]  Ivica Kostanic,et al.  Principles of Neurocomputing for Science and Engineering , 2000 .

[7]  Yousen Xia.  Neural network for solving extended linear programming problems , 1997, IEEE Trans. Neural Networks.

[8]  Derong Liu,et al.  On the global output convergence of a class of recurrent neural networks with time-varying inputs , 2005, Neural Networks.

[9]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[10]  Jinde Cao,et al.  A Delayed Neural Network Method for Solving Convex Optimization Problems , 2006, Int. J. Neural Syst..

[11]  Jun Wang,et al.  A projection neural network and its application to constrained optimization problems , 2002 .

[12]  Bingsheng He.  Solution and applications of a class of general linear variational inequalities , 1996 .

[13]  Xiaolin Hu,et al.  Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks , 2007, IEEE Transactions on Neural Networks.

[14]  Jinde Cao,et al.  Solving Quadratic Programming Problems by Delayed Projection Neural Network , 2006, IEEE Transactions on Neural Networks.

[15]  Elisa Ricci,et al.  Analog neural network for support vector machine learning , 2006, IEEE Transactions on Neural Networks.

[16]  Liqun Qi,et al.  An SQP algorithm for extended linear-quadratic problems in stochastic programming , 1995, Ann. Oper. Res..

[17]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[18]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[19]  R. Tyrrell Rockafellar,et al.  Computational schemes for large-scale problems in extended linear-quadratic programming , 1990, Math. Program..

[20]  Tao Qing,et al.  The Neural Network Model for Solving Minimax Problems with Constraints , 2000 .

[21]  Bingsheng He,et al.  A neural network model for monotone linear asymmetric variational inequalities , 2000, IEEE Trans. Neural Networks Learn. Syst..

[22]  Xiaolin Hu,et al.  Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  Xiaolin Hu,et al.  Solving Extended Linear Programming Problems Using a Class of Recurrent Neural Networks , 2006, ICONIP.

[24]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[25]  R. Rockafellar,et al.  A Lagrangian Finite Generation Technique for Solving Linear-Quadratic Problems in Stochastic Programming , 1986 .

[26]  Jie Sun,et al.  A Predictor-Corrector Algorithm for a Class of Nonlinear Saddle Point Problems , 1997 .

[27]  Li-Zhi Liao,et al.  A Novel Neural Network for a Class of Convex Quadratic Minimax Problems , 2006, Neural Computation.