Nobuo Yamashita

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Abstract. The Second-Order Cone Complementarity Problem (SOCCP) is a wide class of problems containing the Nonlinear Complementarity Problem (NCP) and the Second-Order Cone Programming Problem (SOCP). Recently, Fukushima, Luo and Tseng extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas(More)
Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained di erentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions(More)
We consider the problem of finding a solution of a constrained (and not necessarily square) system of equations, i.e., we consider systems of nonlinear equations and want to find a solution that belongs to a certain feasible set. To this end, we present two Levenberg-Marquardt-type algorithms that differ in the way they compute their search directions. The(More)
Recently, Tseng extended several merit functions for the nonlinear complementarity problem to the semide nite complementarity problem (SDCP) and investigated various properties of those functions. In this paper, we propose a new merit function for the SDCP based on the squared Fischer-Burmeister function and show that it has some favorable properties.(More)
In this paper we formulate the problem of multiuser power control for digital subscriber lines (DSL) as a nonlinear complementarity problem (NCP). We study conditions under which the resulting NCP belongs to the class P0 and its solution is B-regular. The NCP formulation makes it possible to use the Newton type smoothing methods to efficiently compute a(More)
This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a(More)
In this paper, we consider a proximal point algorithm (PPA) for solving monotone nonlinear complementarity problems (NCP). PPA generates a sequence by solving subproblems that are regularizations of the original problem. It is known that PPA has global and superlin-ear convergence property under appropriate criteria for approximate solutions of subproblems.(More)
Exogenous thiamine regulates Aspergillus oryzae thiA, which is involved in thiamine synthesis. One of the two introns in its 5'-untranslated region (5'-UTR) contains motifs (regions A and B) highly conserved among fungal thiamine biosynthesis genes. Deletion of either region relieved the repression by thiamine and thiamine inhibited intron splicing,(More)