TITLE:
A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets
AUTHORS:
Hiroko Okochi
KEYWORDS:
Subdifferential, Convex Functional, Monotone Operator, Resolvent, Lagrange Multiplier, Banach Space, Metric Projection
JOURNAL NAME:
Applied Mathematics,
Vol.14 No.6,
June
30,
2023
ABSTRACT: 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.