A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs
A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs
复制标题
DOI：
10.1007/s10589-022-00402-x
复制
发表时间：
2022-09-16
影响因子：
2.2
通讯作者：
Okuno, Takayuki
中科院分区：
文献类型：
--
作者：
Yamakawa, Yuya;Okuno, Takayuki
本文提出了一种求解退化非线性半定规划的序列二次半定规划（SQSDP）方法，该方法通过求解一系列稳定的二次半定规划（QSDP）子问题来产生迭代点，这些子问题是由与NSDP相关的极大极小问题衍生而来的.与现有的SQSDP方法不同，该方法允许我们不精确地求解这些QSDP子问题，并且每个QSDP都是可行的。该方法的另一个显著特点是在全局收敛性分析中不需要拉格朗日乘子序列的约束条件或有界性。具体来说，没有假设这样的条件下，我们证明了全局收敛到一个点满足以下任何一个：稳定的条件的可行性问题，近似Karush-Kuhn-Tucker（AKKT）条件，和跟踪AKKT条件。最后，我们进行了一些数值实验来检验所提出的方法的效率。
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic semidefinite programming (QSDP) subproblems, which we derive from the minimax problem associated with the NSDP. Unlike the existing SQSDP methods, the proposed one allows us to solve those QSDP subproblems inexactly, and each QSDP is feasible. One more remarkable point of the proposed method is that constraint qualifications or boundedness of Lagrange multiplier sequences are not required in the global convergence analysis. Specifically, without assuming such conditions, we prove the global convergence to a point satisfying any of the following: the stationary conditions for the feasibility problem, the approximate-Karush-Kuhn-Tucker (AKKT) conditions, and the trace-AKKT conditions. Finally, we conduct some numerical experiments to examine the efficiency of the proposed method.