非光滑非单调变分不等式问题的Kurdyka-Schojasiewicz不等式与D-间隙函数的误差界
Kurdyka-Łojasiewicz Inequality and Error Bounds of D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems
摘要：
本文研究了一类非光滑非单调变分不等式问题的D-间隙函数。给出了D-间隙函数的次导数、正则次微分集和极限次微分集的精确公式。利用这些公式，我们给出了D-间隙函数具有Kurdyka-Kauojasiewicz不等式性质和误差界性质的一些充分和必要条件.作为我们的Kurdyka-Kazojasiewicz不等式结果和[Attouch，et al.，半代数和驯服问题的下降法的收敛性：近似算法、向前向后分裂和正则化高斯-赛德尔方法，数学程序，137（2013）91-129]，我们证明了由具有不精确线搜索的导数自由下降算法生成的序列线性地收敛到变分不等式问题的某个解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
