Results 101 to 110 of about 810 (214)

Convergence of subdifferentials and normal cones in locally uniformly convex Banach space

open access: yes, 2014
International audienceIn this paper we study the behaviour of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch–Wets convergences.
Zakaryan, T., Thibault, L.
core   +1 more source

Using of Modified Simplex Imbeddings Method for Solving Special Class of Convex Non-Differentiable Optimization Problems

open access: yesИзвестия Иркутского государственного университета: Серия "Математика", 2015
In this paper it is considered the modified simplex imbeddings method, which is related to the class of cutting plane methods. The main feature of this method is the convergence estimation, which depends only on the quantity of simplex vertices, that are
A.V. Kolosnitcyn
doaj  

The Equivalence of Several Basic Theorems for Subdifferentials

open access: yes
. Several different basic properties are used for developing a system of calculus for subdifferentials. They are a nonlocal fuzzy sum rule in [5, 25], a multidirectional mean value theorem in [7, 8], local fuzzy sum rules in [14, 15] and an extremal ...
Qiji J. Zhu
core  

Separable reductions and rich families in theory of Fréchet subdifferentials

open access: yes, 2015
We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fréchet sense.
Fabian, Marián
core  

Subdifferentials Whose Graphs Are Not Norm × Weak* Closed

open access: yes, 2003
In this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a proper lower semicontinuous convex function on a separable Hilbert space such that the graph of its subdifferential is not ...
Roland Girgensohn   +2 more
core   +1 more source

Two Constraint Qualifications for Non-Differentiable Semi-Infinite Programming Problems Using Fr´echet and Mordukhovich Subdifferentials

open access: yesJournal of Mathematical Extension, 2014
. In this paper, we consider the semi-infinite programming problems with non-differentiable emerging functions. Firstly, we give a counterexample showing that Theorem 3.1 of Ref. [10] is not true. Then, by modifying the assumptions of this theorem, we
N. Kanzi
doaj  

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