SIAM Journal on Optimization, Volume 30, Issue 2, Page 1555-1581, January 2020.
It is a well-known phenomenon that the presence of critical Lagrange multipliers in constrained optimization problems may cause a deterioration of the convergence speed of primal-dual Newton-type methods. Regardless of the method under consideration, we develop a new local technique for avoiding convergence to critical Lagrange multipliers of equality-constrained optimization problems. This technique consists of replacing dual iterates of the methods by a special function of primal iterates. Under some natural assumptions, this function yields an approximation of a Lagrange multiplier, whose quality agrees with the distance from the primal iterate to the respective stationary point, while at the same time staying away from the critical multiplier in question. The accelerating effect of this technique is demonstrated by numerical experiments for stabilized sequential quadratic programming, the Levenberg--Marquardt method, and the LP-Newton method.

中文翻译：

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在临界拉格朗日乘数的情况下调整对偶迭代

SIAM优化杂志，第30卷，第2期，第1555-1581页，2020年1月。
一个众所周知的现象是，约束优化问题中存在关键的拉格朗日乘数可能会导致原始对偶牛顿型方法的收敛速度下降。无论考虑哪种方法，我们都开发了一种新的局部技术，可以避免收敛到等式约束优化问题的关键拉格朗日乘数。该技术包括用原始迭代器的特殊功能替换方法的双重迭代器。在某些自然假设下，此函数会得出拉格朗日乘数的近似值，其质量与从原始迭代器到相应固定点的距离相符，同时又远离所讨论的临界乘数。