A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Some basic properties of the affine variational inequality subproblems in the classical Josephy-Newton method are studied. A hybrid Josephy-Newton method is then proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.
Publié le : 1999-07-04
Classification:
quadratic convergence,
global convergence,
variational inequality problem,
box constraints,
D-gap function,
Newton's method,
unconstrained optimization,
[MATH]Mathematics [math],
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph]
@article{hal-01975369,
author = {Peng, Ji-Ming and KANZOW, CHRISTIAN and Fukushima, Masao},
title = {A hybrid Josephy-Newton method for solving box constrained variational equality problems via the D-gap function},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01975369}
}
Peng, Ji-Ming; KANZOW, CHRISTIAN; Fukushima, Masao. A hybrid Josephy-Newton method for solving box constrained variational equality problems via the D-gap function. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-01975369/