An Interior Point Recurrent Neural Network for Convex Optimization Problems

An interior point recurrent neural network for convex inequality constrained optimization problems is proposed, based on the logarithmic barrier function. A time varying barrier parameter is used and the network’s dynamical equations are based on Newton’s method. Strictly feasible interior point trajectories are produced which converge to the exact solution of the constrained problem as t → ∞. Numerical results for examples of various sizes show that the method is both efficient and accurate.

[1]  Nicholas G. Maratos,et al.  A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems , 2008, IEEE Transactions on Neural Networks.

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

[3]  Michael Peter Kennedy,et al.  Unifying the Tank and Hopfield linear programming circuit and the canonical nonlinear programming circuit of Chua and Lin , 1987 .

[4]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[5]  Malur K. Sundareshan,et al.  Exponential stability and a systematic synthesis of a neural network for quadratic minimization , 1991, Neural Networks.

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

[7]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[8]  Kwong-Sak Leung,et al.  A new gradient-based neural network for solving linear and quadratic programming problems , 2001, IEEE Trans. Neural Networks.

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

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

[11]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[12]  Stefen Hui,et al.  On solving constrained optimization problems with neural networks: a penalty method approach , 1993, IEEE Trans. Neural Networks.

[13]  Yee Leung,et al.  A high-performance feedback neural network for solving convex nonlinear programming problems , 2003, IEEE Trans. Neural Networks.

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

[15]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[16]  Jun Wang,et al.  A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations , 2004, Neural Networks.

[17]  Nicholas G. Maratos,et al.  A neural network for convex optimization , 2006, 2006 IEEE International Symposium on Circuits and Systems.