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

Authors:
Xiaolin Hu
Affiliations:
Tsinghua National Lab for Information Science and Technology, State Key Lab of Intelligent Technology and Systems, and Department of Computer Science and Technology, Tsinghua University, Beijing 1 ...
Venue:
Neurocomputing
Year:
2009

Citing 16
Cited 8

Computational schemes for large-scale problems in extended linear-quadratic programming

Mathematical Programming: Series A and B
A Predictor-Corrector Algorithm for a Class of Nonlinear Saddle Point Problems

SIAM Journal on Control and Optimization
Principles of Neurocomputing for Science and Engineering

Principles of Neurocomputing for Science and Engineering
On the global output convergence of a class of recurrent neural networks with time-varying inputs

Neural Networks
A novel neural network for a class of convex quadratic minimax problems

Neural Computation
Solving extended linear programming problems using a class of recurrent neural networks

ICONIP'06 Proceedings of the 13th international conference on Neural Information Processing - Volume Part II
Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Neural network for solving extended linear programming problems

IEEE Transactions on Neural Networks
A neural network model for monotone linear asymmetric variational inequalities

IEEE Transactions on Neural Networks
A general projection neural network for solving monotone variational inequalities and related optimization problems

IEEE Transactions on Neural Networks
A neural network for a class of convex quadratic minimax problems with constraints

IEEE Transactions on Neural Networks
A delayed neural network for solving linear projection equations and its analysis

IEEE Transactions on Neural Networks
Analog neural network for support vector machine learning

IEEE Transactions on Neural Networks
Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

IEEE Transactions on Neural Networks
Solving Quadratic Programming Problems by Delayed Projection Neural Network

IEEE Transactions on Neural Networks
Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks

IEEE Transactions on Neural Networks

Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
A generalized neural network for solving minimax problems with nonsmooth cost functions

Neurocomputing
A new neural network for solving nonlinear programming problems

ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Convergence of the projection-based generalized neural network and the application to nonsmooth optimization problems

ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Efficient neural networks for solving variational inequalities

Neurocomputing
A capable neural network model for solving the maximum flow problem

Journal of Computational and Applied Mathematics
A new neural network for solving nonlinear convex programs with linear constraints

Neurocomputing
Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

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.