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In this thesis, we consider the unconstrained minimization problem and its related problems, such as the system of equations, the nonlinear least squares problem and the nonlinear complementarity problem (NCP). These problems have various applications in the real world, and they are the fundamental problems in nonlinear optimization problems. Thus, it is worth studying on these problems not only for their own applications but also for constructing more general-purpose solution methods. Many solution methods for solving these problems, such as the steepest descent method and the Newton-type methods, have been proposed. However, there still remain a lot of problems that cannot be solved in practical time by the existing solution methods. Efficiencies of solution methods for our problems are often discussed in terms of the global convergence or the rapid rate of convergence. The global convergence property ensures to get a solution from an arbitrary initial point. On the other hand, the rate of convergence represents the speed to get a solution from a point near the solution. Recently, in addition to these points of view, global complexity bounds of solution methods have received much attention, and have been actively investigated. The global complexity bound is defined as an upper bound of the number of iterations required to get a reasonable solution satisfying appropriate conditions. Since it corresponds to th