双重稀疏约束优化问题的一种贪婪单纯形算法  

The Greedy Simplex Algorithm for Double Sparsity Constrained Optimization Problems

作　　者：潘庭葳 贺素香 Pan Tingwei;He Suxiang(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院数学系,武汉430070

出　　处：《数学物理学报（A辑）》2022年第3期920-933,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871153)~。

摘　　要：鉴于交替最小化方法在求解双重稀疏约束优化问题时需要计算目标函数梯度的Lipschitz常数和构建该问题的L-稳定点时需要借助于Lipschitz条件等方面的不足,该文提出了一种求解该问题的贪婪单纯形算法.刻画了双重稀疏约束优化问题的CW最优性条件.基于CW最优性条件,具体设计了该算法的迭代步骤,并在较弱的假设条件下,证明了由算法产生的迭代点列全局收敛到问题的CW最优解.In view of the shortcomings of the alternating minimization method in which it needs to calculate the Lipschitz constant of the objective function gradient and the Lipschitz condition is needed to construct the L-stable point of the problem,this paper proposes a greedy simplex algorithm to solve the optimization problems with double sparse constraints.The CW optimality condition for double sparse constrained optimization problems is described.Based on the CW optimality condition,the iterative steps of the algorithm are designed,and the global convergence of the sequence of iterative points generated by the algorithm to the optimal solution of the problem is proved under the weaker assumptions.

关 键 词：双重稀疏约束优化问题 CW最优性条件 贪婪单纯形算法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]