凸計画法における解を求める近似法の1つである近接点法は, 1976年にRockafellar等によってHilber空間の場合で始められ, その後多くの研究者によってその研究が行われている。本稿では, その近接点法を増大作用素や単調作用素, 非拡大作用素などの非線形作用素を通してBanach空間で行うとともに, その極限に現れる非線形射影をBanach空間のノルムの凸性や微分可能性などのBanach空間の幾何学と関連した形で行っている。
The proximal point method, one of the approximation methods for finding solutions in convex programming, was started by Rockafellar and others, in the case of Hilbert space in 1976; and thereafter, numerous researchers have been conducting this research.
While this study performs a proximal point method in a Banach space through nonlinear operators such as accretive operators, monotone operators, and by nonlinear operators such as nonexpansive mappings, etc., this study also performs this in connection with the geometry of Banach spaces, such as convexity of Banach spaces, differentiability of norms, etc., the nonlinear projections that emerge at their limits.
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