Local Lipschitz continuity of the metric projection operator
نویسندگان
چکیده
منابع مشابه
On Stability of the Metric Projection Operator
Abstract. Let M be a closed linear subspace of a normed linear space X. For a given f ∈ X denote by PM f the set of best approximations to f from M . The operator PM is termed the metric projection onto M . In this paper we are interested in the stability of the metric projection PM relative to perturbations of the subspace M . We mainly consider the case where X = Lp, p ∈ [1,∞]. We consider a ...
متن کاملLocal Lipschitz Continuity of the Diametric Completion Mapping
The diametric completion mapping associates with every closed bounded set C in a normed linear space the set γ(C) of its completions, that is, of the diametrically complete sets containing C and having the same diameter. We prove local Lipschitz continuity of this set-valued mapping, with respect to two possible arguments: either as a function on the space of closed, bounded and convex sets, wh...
متن کاملLocal strong convexity and local Lipschitz continuity of the gradient of convex functions
Given a pair of convex conjugate functions f and f∗, we investigate the relationship between local Lipschitz continuity of ∇f and local strong convexity properties of f∗.
متن کاملLipschitz Continuity of Liu Process
Liu process is a type of fuzzy process. It is a fuzzy counterpart of Brownian motion. In this paper, the continuity property of Liu process is studied. It is proved that almost all Liu paths are Lipschitz continuous.
متن کاملLipschitz Continuity of inf-Projections
It is shown that local epi-sub-Lipschitz continuity of the function-valued mapping associated with a perturbed optimization problem yields the local Lipschitz continuity of the inf-projections (= marginal functions, = infimal functions). The use of the theorem is illustrated by considering perturbed nonlinear optimization problems with linear constraints.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1979
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-4-1-43-53