A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems
In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisf...
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| Published in | IEEE transactions on neural networks Vol. 19; no. 10; pp. 1665 - 1677 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.10.2008
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1045-9227 1941-0093 1941-0093 |
| DOI | 10.1109/TNN.2008.2000993 |
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| Abstract | In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t rarr infin. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate. |
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| AbstractList | In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t --> infinity. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate. In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t --> infinity. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate.In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t --> infinity. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate. In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t rarr infin. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate. |
| Author | Maratos, N.G. Barbarosou, M.P. |
| Author_xml | – sequence: 1 givenname: M.P. surname: Barbarosou fullname: Barbarosou, M.P. organization: Sch. of Electr. & Comput. Engneering, Nat. Tech. Univ. of Athens, Athens – sequence: 2 givenname: N.G. surname: Maratos fullname: Maratos, N.G. |
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| Keywords | Exponential convergence Recurrent neural nets Non convex programming convergence convex and nonconvex problems Constraint satisfaction Network management Neural network Convex programming Constrained optimization recurrent neural networks Convergence rate Convexity Numerical convergence Non convex analysis Mathematical programming |
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| SubjectTerms | Algorithms Applied sciences Artificial intelligence Circuits Computer science; control theory; systems Computer Simulation Connectionism. Neural networks Constrained optimization Constraint optimization Convergence convex and nonconvex problems Design optimization Exact sciences and technology Feedback Lagrangian functions Models, Theoretical Neural networks Neural Networks (Computer) Nonlinear equations Numerical Analysis, Computer-Assisted Piecewise linear techniques Programming profession Recurrent neural networks |
| Title | A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems |
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