Local Convergence Behavior of Some Projection-Type Methods for Affine Variational Inequalities

J. Z. Zhang and H. H. Xiu
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J. Z. Zhang: City University of Hong Kong
H. H. Xiu: Northern Jiaotong University

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 1, No 9, 205-216

Abstract: Abstract In this paper, we study the local convergence behavior of four projection-type methods for the solution of the affine variational inequality (AVI) problem. It is shown that, if the sequence generated by one of the methods converges to a nondegenerate KKT point of the AVI problem, then after a finite number of iterations, some index sets in the dual variables at each iterative point coincide with the index set of the active constraints in the primal variables at the KKT point. As a consequence, we find that, after finitely many iterations, the four methods need not compute projections and their iterative equations are of reduced dimension.

Keywords: projection-type methods; active constraints; affine variational inequalities (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1026474207884

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