A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets  

作　　者：Hiroko Okochi Hiroko Okochi(Faculty of Pharmacy, Tokyo University of Pharmacy, Tokyo, Japan)

机构地区：[1]Faculty of Pharmacy, Tokyo University of Pharmacy, Tokyo, Japan

出　　处：《Applied Mathematics》2023年第6期428-435,共8页应用数学（英文）

摘　　要：An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions.An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions.

关 键 词：SUBDIFFERENTIAL Convex Functional Monotone Operator RESOLVENT Lagrange Multiplier Banach Space Metric Projection 

分 类 号：O17[理学—数学]