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In this thesis, we study the second-order cone complementarity problem, SOCCP for short. This problem is to find a solution satisfying a system of equations and a complementarity condition defined on the Cartesian product of second-order cones, simultaneously Classical complementarity problems, such as linear complementarity problems, nonlinear com-plementarity problems, and mixed complementarity problems, are defined on the nonnegative or-thant, and have been studied extensively so far. For linear complementarity problems, Lemke’s method was proposed in the 1960’s as an approach to solve convex quadratic programming prob-lems. For nonlinear complementarity problems, studies on the nonsmooth reformulation approach flourished in the 1990’s, in which Fischer-Burmeister function or the min function were employed to construct an equivalent system of nonsmooth equations. On the other hand, studies for SOCCPs have begun only recently. For example, Fukushima, Luo and Tseng introduced a scheme of analyzing SOCCPs by using Jordan algebra. It requires, however, quite different analysis from the classical complementarity problems since the Jordan product is not associative in general. Hence, many problems remain unsolved, and efficient algorithms have yet to be developed. Meanwhile, the SOCCP has a big potential of applications. Althoug