## Modified Projection-Type Methods For Monotone Variational Inequalities (1996)

Venue: | SIAM Journal on Control and Optimization |

Citations: | 25 - 9 self |

### BibTeX

@ARTICLE{Solodov96modifiedprojection-type,

author = {Michael V. Solodov and Paul Tseng},

title = {Modified Projection-Type Methods For Monotone Variational Inequalities},

journal = {SIAM Journal on Control and Optimization},

year = {1996},

volume = {34},

pages = {1814--1830}

}

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### OpenURL

### Abstract

. We propose new methods for solving the variational inequality problem where the underlying function F is monotone. These methods may be viewed as projection-type methods in which the projection direction is modified by a strongly monotone mapping of the form I \Gamma ffF or, if F is affine with underlying matrix M , of the form I + ffM T , with ff 2 (0; 1). We show that these methods are globally convergent and, if in addition a certain error bound based on the natural residual holds locally, the convergence is linear. Computational experience with the new methods is also reported. Key words. Monotone variational inequalities, projection-type methods, error bound, linear convergence. AMS subject classifications. 49M45, 90C25, 90C33 1. Introduction. We consider the monotone variational inequality problem of finding an x 2 X satisfying F (x ) T (x \Gamma x ) 0 8x 2 X; (1) where X is a closed convex set in ! n and F is a monotone and continuous function from ! n to ...