光滑拉格朗日神经网络解决非光滑最优化问题  

Smoothing Lagrange neural network for constrained nonsmooth optimization problems

作　　者：喻昕[1] 于琰[1] 谢缅 

机构地区：[1]广西大学计算机与电子信息学院,南宁530004

出　　处：《计算机应用研究》2014年第5期1349-1352,共4页Application Research of Computers

基　　金：国家自然科学基金资助项目(61063045);广西科技攻关基金资助项目(桂科攻11107006-1);广西教育厅资助项目(TLZ100715)

摘　　要：针对目标函数是局部Lipschitz函数,其可行域由一组等式约束光滑凸函数组成的非光滑最优化问题,通过引进光滑逼近技术将目标函数由非光滑函数转换成相应的光滑函数,进而构造一类基于拉格朗日乘子理论的神经网络,以寻找满足约束条件的最优解。证明了神经网络的平衡点集合是原始非光滑最优化问题关键点集合的一个子集;当原始问题的目标函数是凸函数时,最小点集合与神经网络的平衡点集合是一致的。通过仿真实验验证了理论结果的正确性。The objective function of the nonsmooth optimization problems was locally Lipschitz and the feasible set of that con- sisted of a set of equality constrained smoothing and convex function. The noiasmooth function was conversed into smooth func- tion by being applied with the smoothing approximate techniques. Moreover, it modeled the Lagrange neural network by a class of differential equations, which could be implemented easily. The methodology was based on the Lagrange multiplier theory in optimization and seeked to provide solutions satisfying the necessary conditions of optimality. It proved that any equilibrium point of the network was a subset to the critical point set of primal problems, when the objective function of primal problems was convex, the minimum set coincided with the equilibrium point set of the network. Finally, it presented a simulation exper- iment to illustrate above theoretical finding.

关 键 词：局部LIPSCHITZ函数 光滑逼近技术 平衡点集合 最小点集合 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]