一种新型拉格朗日神经网络解决非光滑优化问题

Novel Lagrange neural network for nonsmooth optimization problems

针对函数是非光滑的问题以及采用固定惩罚项的弊端,利用Clarke广义梯度的理论和Lagrange乘子法的思想,建立了一个微分包含的神经网络模型。此模型是采用罚函数的方法,有效避免了固定项的缺陷。理论证明了网络是有全局解的,并且收敛到原问题的关键点集,对于凸问题来说网络收敛的平衡点就是问题的最优点。最后通过仿真实验验证了理论结果的正确性。

To solve the problems that many functions are nonsmooth and fixed penalty term has its disadvantages, this paper used the Clarke＇ s generalized gradient of the involved functions and Lagrange method, established a gradient system of diffe- rential inclusions. It had a variable penalty term to avoid some disadvantages of fixed penalty term. And the network had a global solution and its trajectory converges to the critical point set of primal problems. Furthermore, if the problem was con- vex, the equilibrium point exactly reconciles the solution of the programming problem. Finally, simulation results illustrate above theoretical finding.