解决一类非光滑伪凸优化问题的新型神经网络  

Novel Neural Network for Dealing with a Kind of Non-smooth Pseudoconvex Optimization Problems

作　　者：喻昕[1] 林植良 YU Xin;LIN Zhi-liang(School of Computer,Electronics and Information,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学计算机与电子信息学院,南宁530004

出　　处：《计算机科学》2022年第5期227-234,共8页Computer Science

基　　金：国家自然科学基金(61862004)。

摘　　要：对优化问题的研究一直以来深受科研工作者的关注。非光滑伪凸优化作为非凸优化中的一类特殊问题,频繁出现在机器学习、信号处理、生物信息学以及各类科学与工程领域中,成为学者们研究的重点。基于罚函数以及微分包含的思想,提出了一种解决带有不等式约束条件和等式约束条件的非光滑伪凸优化问题的新型神经网络方法。在给定的假设条件下,该神经网络的解可以在有限时间内进入可行域并永驻其中,最终收敛到优化问题的最优解集。相比其他神经网络模型,该模型具有以下优点:1)结构简单,为单层模型;2)不需要事先计算精确的惩罚因子;3)初始点可任意选取。在MATLAB环境下,通过数值实验得出,所提网络都能在有限时间内收敛到一个最优解;而用现有的神经网络模型解决同样的优化问题时,若初始点选取不恰当,则会导致状态解不能在有效时间内收敛甚至不能收敛。这不仅进一步地验证了所提神经网络的有效性,同时也说明其具有更广泛的应用范围。The research of optimization problem is favored by researchers.Nonsmooth pseudoconvex optimization problems are a special kind of nonconvex optimization problems,which often appear in machine learning,signal processing,bioinformatics and various scientific and engineering fields.Based on the idea of penalty function and differential inclusion,a new neural network me-thod is proposed to solve the non-smooth pseudoconvex optimization problems with inequality constraints and equality constraints.Under given assumptions,the solution of the RNN can enter in the feasible region in finite time and stay there there-after,at last converge to the optimal solution set of the optimization problem.Compared with other neural networks,the RNN has the following advantages:1)simple structure,it is a single-layer model;2)it is not need to compute an exact penalty parameter in advance;3)the initial point is chosed arbitrarily.Under the environment of MATLAB,mathematical simulation experiments show that state solution can converge to the optimal solution.At the same time,if the initial points are not selected properly,the state solution will not converge in limit time even can not converge.This not only verifies the effectiveness of the proposed RNN,but also shows that the proposed network has a wider range of applications.

关 键 词：微分包含 循环神经网络 非光滑伪凸优化 最优解集 惩罚因子 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]