非光滑稀疏约束优化问题的最优性条件及算法  

Optimality Conditions and Algorithms for Non-smooth Sparse Cons trained Optimization Problems

作　　者：蔡园园 李国成[1] CAI Yuan-yuan;LI Guo-cheng(College of Science,Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《数学的实践与认识》2022年第7期153-164,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(62176073)。

摘　　要：针对目标函数非光滑的稀疏约束优化问题,给出基本可行性和λ-平稳性两个必要最优性条件,利用所给出的必要最优性条件构造出稀疏次梯度投影算法.在理论上分析了算法的收敛性,证明了由该算法所产生序列的任意聚点都是λ-平稳点.最后,通过两个数值实例验证了算法的收敛性、有效性和优化能力.Aiming at the sparse constrained optimization problem with non-smooth objective function,two necessary optimality conditions of basic feasibility and λ-stationarity are given,and a sparse sub-gradient projection algorithm is constructed by using the necessary optimality conditions.The convergence of the algorithm is analyzed theoretically,and it is proved that any cluster point of the sequence generated by the algorithm is λ-stationary point.Finally,the convergence,effectiveness and optimization ability of the algorithm are verified by two numerical examples.

关 键 词：l_(0)-范数 稀疏约束 非光滑 次梯度 稀疏投影 

分 类 号：O224[理学—运筹学与控制论]