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Modified Newton methods for solving a semismooth reformulation of monotone complementary problems
Yamashita, Nobuo
Fukushima, Masao

Data: 1997
Resum: In this paper, we propose a Newton-type method for solving a semismooth reformulation of monotone complementarity problems. In this method, a direction-finding subproblem, which is a system of linear equations, is uniquely solvable at each iteration. Moreover, the obtained search direction always affords a direction of sufficient decrease for the merit function defined as the squared residual for the semismooth equation equivalent to the complementarity problem. We show that the algorithm is globally convergent under some mild assumptions. Next, by slightly modifying the direction-finding problem, we propose another Newton-type method, which may be considered a restricted version of the first algorithm. We show that this algorithm has a superlinear, or possibly quadratic, rate of convergence under suitable assumptions. Finally, some numerical results are presented. .
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Nonlinear complementarity problems ; Merit functions ; Generalized Newton method ; Semismooth functions
Publicat a: Mathematical Programming, vol. 76 n. 3 (1997) p. 469-491, ISSN 0025-5610

23 p, 1.0 MB
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