2004 年 14 巻 3 号 p. 248-258
This paper presents a tutorial introduction to a simple algorithmic solution to the convex optimization problem defined over the fixed point set of nonexpansive mapping in a real Hilbert space. The algorithmic solution was named the hybrid steepest descent method because it is constructed by blending important ideas in the steepest descent method and in the fixed point theory, and generates a sequence converging strongly to the solution of the problem. In this paper, a classical scheme named the projected gradient method is also highlighted for clarifying its limitation and motivations of the above mentioned problem. The remarkable applicability of the method to the broad range of convexly constrained generalized inverse problems is demonstrated based on a recent unified view of the problems.