文章基本信息

标题：Neural Network Approach for Solving Singular Convex Optimization with Bounded Variables
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作者：Rendong Ge ; Lijun Liu ; Yi Xu 等
期刊名称：Open Journal of Applied Sciences
印刷版ISSN：2165-3917
电子版ISSN：2165-3925
出版年度：2013
卷号：3
期号：3
页码：285-292
DOI：10.4236/ojapps.2013.33036
出版社：Scientific Research Publishing
摘要：Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.
关键词：Neural Networks;Singular Nonlinear Optimization;Stationary Point;Augmented Lagrangian Function;Convergence; LaSalle’s Invariance Principle Plain