Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
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DOI：
10.1007/bf02680550
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发表时间：
1998-09
影响因子：
2.7
通讯作者：
C. Kanzow;M. Fukushima
中科院分区：
文献类型：
--
作者：
C. Kanzow;M. Fukushima
D-gap函数最近由Peng提出，并由Yamashita等人进一步研究，允许一般变分不等式问题的光滑无约束最小化重新表述。本文研究了盒上变分不等式问题或等价的混合互补问题的D-间隙函数。本文件有两个目的。首先，我们深入研究了D-间隙函数的理论性质，如驻点的最优性、有界水平集、全局误差界和广义Hessian。接下来，我们提出了一个非光滑高斯-牛顿型算法最小化的D-间隙函数，并报告了广泛的数值结果，在MCPLIB测试问题集合的整个问题集。
The D-gap function, recently introduced by Peng and further studied by Yamashita et al., allows a smooth unconstrained minimization reformulation of the general variational inequality problem. This paper is concerned with the D-gap function for variational inequality problems over a box or, equivalently, mixed complementarity problems. The purpose of this paper is twofold. First we investigate theoretical properties in depth of the D-gap function, such as the optimality of stationary points, bounded level sets, global error bounds and generalized Hessians. Next we present a nonsmooth Gauss-Newton type algorithm for minimizing the D-gap function, and report extensive numerical results for the whole set of problems in the MCPLIB test problem collection.