Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems
Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems
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DOI：
10.1007/s10107-006-0007-2
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发表时间：
2007-03
影响因子：
2.7
通讯作者：
K. Ng;L. Tan
中科院分区：
文献类型：
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作者：
K. Ng;L. Tan
研究了欧氏空间中闭凸集上的局部Lipschitz但不一定可微函数所定义的变分不等式问题（VIP）的正则化间隙函数（以及一些修正的间隙函数）的Clarke-Rockafellar方向导数.作为应用，我们证明了在强单调性假设下，正则化间隙函数具有分数阶误差界，从而证明了Armijo型算法所提供的序列收敛于（VIP）的解.
We study the Clarke–Rockafellar directional derivatives of the regularized gap functions (and of some modified ones) for the variational inequality problem (VIP) defined by a locally Lipschitz but not necessarily differentiable function on a closed convex set in an Euclidean space. As applications we show that, under the strong monotonicity assumption, the regularized gap functions have fractional exponent error bounds and consequently that the sequences provided by an algorithm of Armijo type converge to the solution of the (VIP).