论文标题
kurdyka-stourjasiewicz不平等和误差范围，用于非平滑和非单调变化不平等问题的D-GAP功能
Kurdyka-Łojasiewicz Inequality and Error Bounds of D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems
论文作者
论文摘要
在本文中，我们研究了与非平滑和非单调变异不平等问题相关的D-GAP函数。我们提供了一些针对下属的公式，常规的亚差异集和D-a-abap函数的限制亚差异集。借助这些公式，我们为kurdyka-łojasiewicz不平等属性和D-GAP函数的错误约束属性提供了一些足够和必要的条件。作为我们的kurdyka-sturejasiewicz的不平等结果和抽象收敛的应用，导致[Attouch等人，半代数和驯服问题的下降方法的收敛：近端算法，前向后退散布以及正常化的高斯 - seidel方法，数学。 Program。，137（2013）91-129]，我们表明，带有不精确线搜索的衍生自由下降算法生成的序列线性收敛到变异不平等问题的某些解决方案。
In this paper, we study the D-gap function associated with a nonsmooth and nonmonotone variational inequality problem. We present some exact formulas for the subderivative, the regular subdifferential set, and the limiting subdifferential set of the D-gap function. By virtue of these formulas, we provide some sufficient and necessary conditions for the Kurdyka-Łojasiewicz inequality property and the error bound property for the D-gap functions. As an application of our Kurdyka-Łojasiewicz inequality result and the abstract convergence result in [Attouch, et al., Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods, Math. Program., 137(2013)91-129], we show that the sequence generated by a derivative free descent algorithm with an inexact line search converges linearly to some solution of the variational inequality problem.
