Application of projection neural network in solving convex programming problems

In this paper we present that solution of convex programming problems is equivalent with solution of projection formulation, then we introduce neural network models for solving projection formulation and analysis stability conditions and convergence. Simulation shows that the introduced neural network is effective in solving convex programming problems.

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

[2]  Jong-Shi Pang,et al.  A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem , 1987, Math. Oper. Res..

[3]  Michael A. Shanblatt,et al.  Linear and quadratic programming neural network analysis , 1992, IEEE Trans. Neural Networks.

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

[5]  P. Tseng,et al.  Modified Projection-Type Methods for Monotone Variational Inequalities , 1996 .

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

[7]  Stefen Hui,et al.  Solving linear programming problems with neural networks: a comparative study , 1995, IEEE Trans. Neural Networks.

[8]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[9]  Giovanna Castellano,et al.  An iterative pruning algorithm for feedforward neural networks , 1997, IEEE Trans. Neural Networks.

[10]  Jun Wang,et al.  A recurrent neural network for solving linear projection equations , 2000, Neural Networks.

[11]  Masao Fukushima,et al.  Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems , 1992, Math. Program..

[12]  Insley B. Pyne,et al.  Linear programming on an electronic analogue computer , 1956, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[13]  Torbjörn Larsson,et al.  A class of gap functions for variational inequalities , 1994, Math. Program..

[14]  Youshen Xia,et al.  Neural network for solving linear programming problems with bounded variables , 1995, IEEE Trans. Neural Networks.

[15]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

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

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

[18]  James David,et al.  Remote Control , 2008 .

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

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

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

[22]  W K Chen,et al.  A high-performance neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

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

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

[25]  Tara Stuckless,et al.  Brouwer's Fixed Point Theorem: Methods of Proof and Generalizations , 2003 .