Although QP-free algorithms have good theoretical convergence and are effective in practice, their applications to minimax optimization have not yet been investigated. In this article, on the basis of the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints. By means of a new and much tighter working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix. At each iteration, to obtain the search direction, two reduced systems of linear equations with the same coefficient are solved. Under mild conditions, the proposed algorithm is globally convergent. Finally, some preliminary numerical experiments are reported, and these show that the algorithm is promising.

中文翻译：

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不等式约束极大极小优化的全局收敛无QP算法

尽管 QP-free 算法具有良好的理论收敛性并且在实践中是有效的，但尚未研究它们在极小极大优化中的应用。在本文中，在平稳条件的基础上，没有指数平滑函数或约束平滑变换，我们提出了一种具有不等式约束的非线性极大极小优化的无QP算法。通过一个新的更紧密的工作集，我们开发了一种新的技术来构造系数矩阵右下角的子矩阵。在每次迭代中，为了获得搜索方向，求解具有相同系数的两个简化的线性方程组。在温和条件下，所提出的算法是全局收敛的。最后，报告了一些初步的数值实验，