A hybrid Newton method for solving the variational inequality problem via the D-gap function

被引：60

作者：

Peng, JM

Fukushima, M

机构：

[1] Delft Univ Technol, Fac Tech Math & Informat, NL-2628 CD Delft, Netherlands

[2] Acad Sinica, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China

[3] Kyoto Univ, Grad Sch Informat, Dept Appl Math & Phys, Kyoto 6068501, Japan

来源：

MATHEMATICAL PROGRAMMING | 1999年 / 86卷 / 02期

关键词：

variational inequality problem; D-gap function; Newton's method; unconstrained optimization; global convergence; quadratic convergence;

D O I：

10.1007/s101070050094

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the D-gap function. It is proved that the D-gap function has bounded level sets for the strongly monotone VIP. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under some conditions, it is shown that the algorithm is globally convergent and locally quadratically convergent.

引用

页码：367 / 386

页数：20

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