摘要
伪凸优化出现在科学与工程的众多领域,应用广泛。为解决凸不等式约束的非光滑伪凸优化问题,基于微分包含理论,提出了不带精确罚因子的神经网络模型。证明了网络的状态向量在有限时间内进入可行域且永驻其中,并收敛到原优化问题的最优解集。通过两个仿真实例,验证了网络的优化性能。与已有文献不同,采用变步长,收敛效率有了极大的提升。此外,给出了变步长的选取原则及两个选取公式。
Pseudoconvex optimization has been widely used in many fields of science and engineering.A neural network model based on differential inclusion theory and without any exact penalty factor,is proposed for solving nonsmooth pseudoconvex optimization problems which subject to convex inequality constraints.It is proved that the state vector of the network enters into the feasible region in finite time and stays there thereafter,and finally converges to the optimal solution set of the original optimization problem.Two simulation examples are provided to illustrate the performances of the proposed neural network.Different from the existing literature,the convergence efficiency of the network has been greatly improved by using variable-step.In addition,the selection principle and two selection formulas of the variable-step are given.
作者
张坚
李国成
ZHANG Jian;LI Guocheng(School of Applied Sciences,Beijing Information Science&Technology University,Beijing 100192,China)
出处
《北京信息科技大学学报（自然科学版）》
2021年第3期24-33,44,共11页
Journal of Beijing Information Science and Technology University
基金
国家自然科学基金资助项目(61473325)。
关键词
伪凸优化问题
微分包含
神经网络
变步长
pseudoconvex optimization problem
differential inclusion
neural network
variable-step
