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Title: Some numerical algorithms for monotone variational inequalities
Other Titles: Jie dan diao bian fen bu deng shi de yi xie shu zhi suan fa
Authors: Yuan, Xiaoming (袁曉明)
Department: Dept. of Mathematics
Degree: Doctor of Philosophy
Issue Date: 2004
Publisher: City University of Hong Kong
Subjects: Variational inequalities (Mathematics)
Notes: CityU Call Number: QA316.Y83 2004
Includes bibliographical references (leaves [165]-179)
Thesis (Ph.D.)--City University of Hong Kong, 2004
iv, 179 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: This dissertation presents some numerical algorithms for monotone variational inequalities (VI) in the finite-dimensional space Rm. First, some projection-type algorithms are presented. The applications to the complementarity problems, the p-norm Steiner Minimum Trees problems and the tra±c equilibrium prob- lems show that these projection-type methods are effective in practice. These techniques for VI are then extended to finding a root of a maximal monotone op- erator; therefore a hybrid extragradient-proximal algorithm is presented. Then, the well-known proximal point algorithm is applied to solve the sub-VIs of the augmented Lagrangian method for monotone VI with linear constraints; and thus a proximal augmented Lagrangian method is presented. An inexact version of the proximal augmented Lagrangian method solving the sub-VIs approximately is also provided. Finally, some inexact proximal-type decomposition algorithms are presented for monotone VI with separate structures. In particular, some new practical inexact criteria for solving the sub-VIs are presented. Finally, some conclusions are made and some directions for future research are presented.
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