SIAM Journal on Optimization, Volume 30, Issue 3, Page 2163-2196, January 2020.
We propose a general trust-region method for the minimization of nonsmooth and nonconvex, locally Lipschitz continuous functions that can be applied, e.g., to optimization problems constrained by elliptic variational inequalities. The convergence of the considered algorithm to C-stationary points is verified in an abstract setting and under suitable assumptions on the involved model functions. For a special instance of a variational inequality constrained problem, we are able to properly characterize the Bouligand subdifferential of the reduced cost function, and, based on this characterization result, we construct a computable trust-region model which satisfies all hypotheses of our general convergence analysis. The article concludes with numerical experiments that illustrate the main properties of the proposed algorithm.

中文翻译：

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局部Lipschitz函数的非光滑信赖域方法及其在变分不等式约束的优化问题中的应用

SIAM优化杂志，第30卷，第3期，第2163-2196页，2020年1月。
我们提出了一种通用的信任区域方法，用于最小化不光滑和不凸的局部Lipschitz连续函数，该函数可以应用于例如椭圆变分不等式约束的优化问题。在抽象设置中并在有关模型函数的适当假设下，验证了所考虑算法对C平稳点的收敛性。对于变分不等式约束问题的特殊情况，我们能够正确刻画降成本函数的Bouligand次微分，并根据此刻画结果，构建一个可计算的信任区域模型，该模型满足我们一般收敛的所有假设分析。本文以数值实验作为结束，这些实验说明了所提出算法的主要特性。