david chan

Iterative methods for variational and complementarity problems

Mathematical Programming, 1982

In this paper, we study both the local and global convergence of various iterative methods for so... more In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

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The Generalized Quasi-Variational Inequality Problem

Mathematics of Operations Research, 1982

... E yt(x?) such that for all x with x EK(x), we have (y - yo) (x -x?) > allx - x01\2 for all... more

Iterative Methods for Variational and Complementary Problems

Mathematical Programming, 1982

In this paper, we study both the local and global convergence of various iterative methods for so... more In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

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