Autor: Pallaschke, Diethard - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Algebraic Separation and Shadowing of Arbitrary Sets
Autorzy:: Grzybowski, Jerzy
Pallaschke, Diethard
Urbański, Ryszard
Powiązania:: https://bibliotekanauki.pl/articles/1912878.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: separation
geometry of convex sets
Demyanov difference
data-classification
Opis:: In this paper we consider a generalization of the separation technique proposed in [10,4,7] for the separation of finitely many compact convex sets $A_i,~i \in I $ by another compact convex set $S$ in a locally convex vector space to arbitrary sets in real vector spaces. Then we investigate the notation of shadowing set which is a generalization of the notion of separating set and construct separating sets by means of a generalized Demyanov-difference in locally convex vector spaces.
Źródło:: Commentationes Mathematicae; 2013, 53, 2; 155-164
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Point derivations for Lipschitz functions andClarkes generalized derivative
Autorzy:: Demyanov, Vladimir
Pallaschke, Diethard
Powiązania:: https://bibliotekanauki.pl/articles/1339173.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: point derivations
generalized directional derivative
Lipschitz functions
Opis:: Clarke's generalized derivative $f^0(x,v)$ is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz's product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
Źródło:: Applicationes Mathematicae; 1996-1997, 24, 4; 465-474
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Quasidifferentiable Calculus and Minimal Pairs of Compact Convex Sets
Autorzy:: Pallaschke, Diethard
Urbański, Ryszard
Powiązania:: https://bibliotekanauki.pl/articles/1373556.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:: nonsmooth optimization
generalized convexity
Opis:: The quasidifferential calculus developed by V.F. Demyanov and A.M. Rubinov provides a complete analogon to the classical calculus of differentiation for a wide class of nonsmooth functions. Although this looks at the first glance as a generalized subgradient calculus for pairs of subdifferentials it turns out that, after a more detailed analysis, the quasidifferential calculus is a kind of Fréchet-differentiation whose gradients are elements of a suitable Minkowski–Rådström–Hörmander space. One aim of the paper is to point out this fact. The main results in this direction are Theorem 1 and Theorem 5. Since the elements of the Minkowski–Rådström–Hörmander space are not uniquely determined, we focus our attention in the second part of the paper to smallest possible representations of quasidifferentials, i.e. to minimal representations. Here the main results are two necessary minimality criteria, which are stated in Theorem 9 and Theorem 11.
Źródło:: Schedae Informaticae; 2012, 21; 107-125
0860-0295
2083-8476
Pojawia się w:: Schedae Informaticae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Some remarks on the space of differences of sublinear functions
Autorzy:: Bartels, Sven
Pallaschke, Diethard
Powiązania:: https://bibliotekanauki.pl/articles/1340588.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: upper convex approximation
sublinear function
Fenchel conjugation
quasidifferentiable function
Opis:: Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.
Źródło:: Applicationes Mathematicae; 1993-1995, 22, 3; 419-426
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Spaces of Lipschitz functions on metric spaces
Autorzy:: Pallaschke, Diethard
Pumplün, Dieter
Powiązania:: https://bibliotekanauki.pl/articles/729633.pdf
Data publikacji:: 2015
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: categories of Lipschitz spaces
Saks spaces
base normed spaces
Opis:: In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 5-23
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: Support functions and subdifferentials
Autorzy:: Grzybowski, Jerzy
Pallaschke, Diethard
Urbański, Ryszard
Powiązania:: https://bibliotekanauki.pl/articles/745188.pdf
Data publikacji:: 2016
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Minkowski duality
subdifferential
support function
sublinear function
closed convex sets
Opis:: In this paper we study Minkowski duality, i.e. the correspondence between sublinear functions and closed convex sets in the context of dual pairs of vector spaces.
Źródło:: Commentationes Mathematicae; 2016, 56, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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