非线性半定规划的一个可行SSDP算法
A Feasible SSDP Algorithm for Nonlinear Semidefinite Programming
DOI: 10.12677/AAM.2020.92027, PDF,    国家自然科学基金支持
作者: 何美玲, 黎健玲：广西大学数学与信息科学学院，广西 南宁
关键词: 非线性半定规划；可行SSDP；线搜索；全局收敛性；Nonlinear Semidefinite Programming； Feasible SSDP； Line Search； Global Convergence
摘要: 本文提出了一个求解非线性半定规划的可行序列半定规划(SSDP)算法。该算法的初始点和迭代点均是可行点，在每次迭代中通过求解两个二次半定规划子问题确定搜索方向，步长由满足目标函数下降性和约束函数可行性的线搜索产生，在某些假设条件下本文证明了算法的全局收敛性。
Abstract: This paper proposes a feasible SSDP algorithm for solving nonlinear semidefinite programming. The initial point and iteration points are feasible. The search direction is determined by solving two quadratic semidefinite programming subproblems. The step size is obtained by calculating the line search that satisfies the descent property of the objective function and the feasibility of the constraint function. The global convergence of the algorithm is proved under mild conditions.
文章引用：何美玲, 黎健玲. 非线性半定规划的一个可行SSDP算法[J]. 应用数学进展, 2020, 9(2): 238-243. https://doi.org/10.12677/AAM.2020.92027

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