Subgradient-based feedback neural networks for non-differentiable convex optimization problems |
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基金项目: | 国家研究发展基金;中国科学院资助项目 |
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摘 要: | 1 Introduction Optimization problems arise in a broad variety of scientific and engineering applica- tions. For many practice engineering applications problems, the real-time solutions of optimization problems are mostly required. One possible and very pr…
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收稿时间: | 31 December 2004 |
修稿时间: | 24 November 2005 |
Subgradient-based feedback neural networks for non-differentiable convex optimization problems |
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Authors: | LI Guocheng SONG Shiji WU Cheng |
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Affiliation: | Center of Intelligent and Networked Systems, Department of Automation, Tsinghua University, Beijing 100084, China |
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Abstract: | This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-differentiable convex optimization problems. For unconstrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive, we proved that with ar- bitrarily given initial value, the trajectory of the feedback neural network constructed by a projection subgradient converges to an asymptotically stable equilibrium point which is also an optimal solution of the primal unconstrained problem. For constrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive and the constraint functions are convex also, the energy func- tions sequence and corresponding dynamic feedback subneural network models based on a projection subgradient are successively constructed respectively, the convergence theorem is then obtained and the stopping condition is given. Furthermore, the effective algorithms are designed and some simulation experiments are illustrated. |
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Keywords: | projection subgradient non-differentiable convex optimization convergence feedback neural network |
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