极大极小问题的光滑化信赖域共轭梯度法

A smoothing trust-region Newton-CG method for minimax problems

目的求解无约束有限极大极小问题。方法利用光滑函数将极大极小问题转化为可微的无约束优化问题。结果给出了信赖域牛顿共轭梯度法解该优化问题的算法。结论该算法是可行的、有效的,尤其是对于大规模问题,该算法与其他方法相比具有明显的优势。

Aim To solve the finite unconstrained minimax problems.Methods Exploiting a new smoothing function and converting the minimax problem to an unconstrained optimization problem equivalently.Results A smoothing trust region Newton-CG method for the solution of unconstrained problems is derived.Conclusion Numerical results indicate the feasibility and efficiency of the proposed algoritlm,especially,it is better than the other methods for the large scale problems.