非线性半定规划一个新的全局收敛算法
A New Globally Convergent Algorithm for Nonlinear Semidefinite Programming
DOI: 10.12677/AAM.2018.74056, PDF,    国家自然科学基金支持
作者: 张 辉, 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；SSDP算法；KKT点；全局收敛性；Nonlinear Semidefinite Programming； SSDP Algorithm； KKT Point； Global Convergence
摘要: 本文提出了一个求解非线性半定规划的序列二次半定规划(SSDP)算法。算法每次迭代通过求解两个半定规划子问题确定搜索方向；通过引进距离函数来构造效益函数用于线搜索，从而产生新的迭代点。在适当的假设条件下，算法或收敛到问题的不可行稳定点，或收敛到问题的KKT点。
Abstract: In this paper, we present a sequence quadratic semidefinite programming (SSDP) algorithm for nonlinear semidefinite programming. At each iteration, the search direction is determined by solving two semidefinite programming sub problems; by introducing a distance function, a merit function is constructed for line search. Under some appropriate conditions, any accumulation point of iterative point sequence is either an infeasible stationary point, or a KKT point of the problem.
文章引用：张辉, 黎健玲. 非线性半定规划一个新的全局收敛算法[J]. 应用数学进展, 2018, 7(4): 456-465. https://doi.org/10.12677/AAM.2018.74056

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