Generalized gradient projection neural networks for nonsmooth optimization problems

查看全文 作　　者：LI [1]GuoCheng;SONG [2]ShiJi;WU [2]Cheng

机构地区：[1]Department of Mathematics, Beijing Information Science and Technology University, Beijing 100192, China;[2]Department of Automation, Tsinghua University, Beijing 100084, China

出　　处：《Science China(Information Sciences)》索引2010年第53卷第5期,共16页

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 60874071, 60834004);the National High-Tech Research & Development Program of China (Grant No. 2007AA04Z102);China Ocean Mineral Resources R and D Association Project (Grant No. DYXM-115-03-3-01);Beijing Municipal Education Committee Project (Grant Nos. KM 200711232009, 7100911003) 摘　　要：Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper. 关键词：非光滑优化问题神经网络模型广义梯度投影凸优化问题非线性规划问题全局收敛微分包含原始问题

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Generalized gradient projection neural networks for nonsmooth optimization problems

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