非线性极大极小问题一个新的QP-free算法

A New QP-Free Algorithm for Nonlinear Minimax Problems

本文研究非线性无约束极大极小优化问题. QP-free算法是求解光滑约束优化问题的有效方法之一,但用于求解极大极小优化问题的成果甚少.基于原问题的稳定点条件,既不需含参数的指数型光滑化函数,也不要等价光滑化,提出了求解非线性极大极小问题一个新的QP-free算法.新算法在每一次迭代中,通过求解两个相同系数矩阵的线性方程组获得搜索方向.在合适的假设条件下,该算法具有全局收敛性.最后,初步的数值试验验证了算法的有效性.

In this paper, we discuss the nonlinear unconstrained minimax problems. Although QPfree algorithm is one of the effective methods for solving smooth constrained optimization, the application to minimax problems has not yet been investigated. Based on the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax problems. At each iteration, two reduced systems of linear equations with a same coefficient are solved to obtain the search direction. Under mild conditions, the proposed algorithm is globally convergent. Finally, some numerical experiments show that the algorithm is promising.