A novel neural network for solving convex quadratic programming problems subject to equality and inequality constraints

This paper proposes a neural network model for solving convex quadratic programming (CQP) problems, whose equilibrium points coincide with Karush-Kuhn-Tucker (KKT) points of the CQP problem. Using the equality transformation and Fischer-Burmeister (FB) function, we construct the neural network model and present the KKT condition for the CQP problem. In contrast to two existing neural networks for solving such problems, the proposed neural network has fewer variables and neurons, which makes circuit realization easier. Moreover, the proposed neural network is asymptotically stable in the sense of Lyapunov such that it converges to an exact optimal solution of the CQP problem. Simulation results are provided to show the feasibility and efficiency of the proposed network.

[1]  Bart Kosko,et al.  Neural networks for signal processing , 1992 .

[2]  M. Raja.  Stochastic numerical treatment for solving Troesch’s problem , 2014 .

[3]  Chafic Mokbel,et al.  Handwritten word recognition using Web resources and recurrent neural networks , 2015, International Journal on Document Analysis and Recognition (IJDAR).

[4]  Hongyong Zhao,et al.  A new delayed projection neural network for solving quadratic programming problems with equality and inequality constraints , 2015, Neurocomputing.

[5]  Henry Leung,et al.  Neural data fusion algorithms based on a linearly constrained least square method , 2002, IEEE Trans. Neural Networks.

[6]  Sohrab Effati,et al.  Neural network models and its application for solving linear and quadratic programming problems , 2006, Appl. Math. Comput..

[7]  Sohrab Effati,et al.  A new nonlinear neural network for solving convex nonlinear programming problems , 2005, Appl. Math. Comput..

[8]  S. Sastry.  Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[9]  Abdul-Majid Wazwaz,et al.  Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes , 2016, Appl. Soft Comput..

[10]  D. Serre.  Matrices: Theory and Applications , 2002 .

[11]  Junaid Ali Khan,et al.  Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks , 2015 .

[12]  Sohrab Effati,et al.  An application of a merit function for solving convex programming problems , 2013, Comput. Ind. Eng..

[13]  Jun Wang,et al.  A general methodology for designing globally convergent optimization neural networks , 1998, IEEE Trans. Neural Networks.

[14]  M. Raja,et al.  Design of bio-inspired computational intelligence technique for solving steady thin film flow of Johnson–Segalman fluid on vertical cylinder for drainage problems , 2016 .

[15]  J. Wang.  Recurrent neural network for solving quadratic programming problems with equality constraints , 1992 .

[16]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[17]  Ai Wu,et al.  A Neural Network Methodology and Strategy of Quadratic Optimisation , 1999, Neural Computing & Applications.

[18]  Junfei Qiao,et al.  Nonlinear Model Predictive Control Based on a Self-Organizing Recurrent Neural Network , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Jinde Cao,et al.  A Delayed Lagrangian Network for Solving Quadratic Programming Problems with Equality Constraints , 2006, ISNN.

[20]  Syed Muslim Shah,et al.  Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem , 2015 .

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

[22]  Masao Fukushima,et al.  Smoothing Functions for Second-Order-Cone Complementarity Problems , 2002, SIAM J. Optim..

[23]  Jinde Cao,et al.  Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints , 2011, Neurocomputing.

[24]  Alaeddin Malek,et al.  Image fusion algorithms for color and gray level images based on LCLS method and novel artificial neural network , 2010, Neurocomputing.

[25]  Jein-Shan Chen,et al.  A semismooth Newton method for SOCCPs based on a one-parametric class of SOC complementarity functions , 2010, Comput. Optim. Appl..

[26]  Ricardo A. S. Fernandes,et al.  Maximum and minimum stock price forecasting of Brazilian power distribution companies based on artificial neural networks , 2015, Appl. Soft Comput..

[27]  Paulo J. G. Lisboa,et al.  Hybrid Neural Network Predictive-Wavelet Image Compression System , 2015, Neurocomputing.

[28]  Sohrab Effati,et al.  An efficient projection neural network for solving bilinear programming problems , 2015, Neurocomputing.

[29]  Yuancan Huang,et al.  Lagrange-Type Neural Networks for Nonlinear Programming Problems with Inequality Constraints , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[30]  Jinde Cao,et al.  A new neural network for solving quadratic programming problems with equality and inequality constraints , 2014, Math. Comput. Simul..

[31]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[32]  Hani Hamdan,et al.  Artificial neural network dexterous robotics hand optimal control methodology: grasping and manipulation forces optimization , 2010, Artificial Life and Robotics.

[33]  Shengwei Zhang,et al.  Lagrange programming neural networks , 1992 .

[34]  Defeng Sun,et al.  A class of iterative methods for solving nonlinear projection equations , 1996 .

[35]  Liwei Zhang,et al.  A globally convergent method based on Fischer-Burmeister operators for solving second-order cone constrained variational inequality problems , 2009, Comput. Math. Appl..

[36]  Dimitrios Zissis,et al.  A cloud based architecture capable of perceiving and predicting multiple vessel behaviour , 2015, Appl. Soft Comput..

[37]  Alireza Nazemi.  A neural network model for solving convex quadratic programming problems with some applications , 2014, Eng. Appl. Artif. Intell..

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

[39]  Alireza Nazemi,et al.  A Gradient-Based Neural Network Method for Solving Strictly Convex Quadratic Programming Problems , 2014, Cognitive Computation.

[40]  Abdul-Majid Wazwaz,et al.  Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory , 2015, Connect. Sci..

[41]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[42]  Tiesong Hu,et al.  A neural network approach for solving nonlinear bilevel programming problem , 2008, Comput. Math. Appl..

[43]  Sheng-Long Hu,et al.  Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems , 2009 .

[44]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[45]  Jein-Shan Chen,et al.  Neural networks for solving second-order cone constrained variational inequality problem , 2012, Comput. Optim. Appl..

[46]  Edgar Sanchez-Sinencio,et al.  Nonlinear switched capacitor 'neural' networks for optimization problems , 1990 .

[47]  Muhammad Asif Zahoor Raja,et al.  Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP , 2014 .

[48]  Qingshan Liu,et al.  A Projection Neural Network for Constrained Quadratic Minimax Optimization , 2015, IEEE Transactions on Neural Networks and Learning Systems.