This paper proposes a globally convergent regularized interior point method that involves a specifically designed regularization strategy for constrained optimization. The main concept of the proposed algorithm is that when a proper regularization parameter is selected, the direction obtained from the regularized barrier equation is a descent direction for either the objective function or constraint violation. Accordingly, by embedding a flexible strategy of choosing a regularization parameter in a trust-funnel-like interior point scheme, we propose the new algorithm. Global convergence under the mild assumptions of relaxed constant rank constraint qualification (RCRCQ) and local consistency of the linearized active and equality constraints is shown. Preliminary numerical experiments are conducted, and the results are encouraging.

本文提出了一种全局收敛的正则化内点方法，该方法涉及一种专门设计的用于约束优化的正则化策略。所提出的算法的主要概念是被选择一个适当的正则化参数的情况下，从正则化屏障式求出方向为任一目标函数或约束违反下降方向。因此，通过在类似信任漏斗的内部点方案中嵌入选择正则化参数的灵活策略，我们提出了一种新算法。显示了在宽松的恒定秩约束条件（RCRCQ）和线性化主动约束条件和相等约束条件的局部一致性的适度假设下的全局收敛性。进行了初步的数值实验，结果令人鼓舞。