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    Wyświetlanie 1-11 z 11
    Tytuł:
    Schramm spaces and composition operators
    Autorzy:
    Wróbel, Małgorzata
    Powiązania:
    https://bibliotekanauki.pl/articles/24201507.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Schramm function
    continuous function
    Nemytskij composition operator
    Schramm type variation
    uniformly continuous operator
    Lipschitz operator
    funkcja Schramma
    funkcja ciągła
    operator kompozycji Niemyckiego
    operator jednostajnie ciągły
    operator Lipschitza
    Opis:
    We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 87--98
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Characterizations and classification of paraconvex multimaps
    Autorzy:
    Mokhtar-Kharroubi, Hocine
    Powiązania:
    https://bibliotekanauki.pl/articles/2183481.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    support function
    paraconvex multimap
    Lipschitz property
    generalized convexities
    submonotonicity
    Opis:
    Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.
    Źródło:
    Control and Cybernetics; 2022, 51, 3; 303--325
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations
    Autorzy:
    Hante, Falk M.
    Schmidt, Martin
    Powiązania:
    https://bibliotekanauki.pl/articles/1839150.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimization
    differential equations
    optimal value function
    Lipschitz continuity
    parametric optimization
    mixed integer nonlinear programming
    Opis:
    We consider a direct approach to solving the mixedinteger nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the step size for discretization of the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks.
    Źródło:
    Control and Cybernetics; 2019, 48, 2; 209-226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimality conditions and duality for generalized fractional minimax programming involving locally Lipschitz (b,Ψ,Φ,ρ) -univex functions
    Autorzy:
    Antczak, T.
    Mishra, S. K.
    Upadhyay, B. B.
    Powiązania:
    https://bibliotekanauki.pl/articles/206666.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    generalized fractional minimax programming
    locally Lipschitz (b,Ψ,Φ,ρ)-univex function
    optimality conditions
    duality
    Opis:
    In this paper, we are concerned with optimality conditions and duality results of generalized fractional minimax programming problems. Sufficient optimality conditions are established for a class of nondifferentiable generalized fractional minimax programming problems, in which the involved functions are locally Lipschitz (b,Ψ,Φ,ρ)-univex. Subsequently, these optimality conditions are utilized as a basis for constructing various parametric and nonparametric duality models for this type of fractional programming problems and proving appropriate duality theorems.
    Źródło:
    Control and Cybernetics; 2018, 47, 1; 5-32
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
    Autorzy:
    Delfour, M. C.
    Powiązania:
    https://bibliotekanauki.pl/articles/970297.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    thin shell
    asymptotic shell
    midsurface
    smoothness
    representation of a surface
    oriented distance function
    bi-Lipschitz mapping
    tubular neighborhood
    Opis:
    Many hypersurfaces ω in R^N can be viewed as a subset of the boundary Γ of an open subset Ω of R^N. In such cases, the gradient and Hessian matrix of the associated oriented distance function ba to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C1'1-hypersurfaces is available in Delfour (2000). In the theory of thin shells, the asymptotic model only depends on the choice of the constitutive law, the midsurface, and the space of solutions that properly handles the loading applied to the shell and the boundary conditions. A central issue is the minimal smoothness of the midsurface to still make sense of asymptotic membrane shell and bending equations without ad hoc mechanical or mathematical assumptions. This is possible for a C1'1-midsurface with or without boundary and without local maps, local bases, and Christoffel symbols via the purely intrinsic methods developed by Delfour and Zolesio (1995a) in 1992. Anicic, LeDret and Raoult (2004) introduced in 2004 a family of surfaces ω that are the image of a connected bounded open Lipschitzian domain in R² by a bi-Lipschitzian mapping with the assumption that the normal field is globally Lipschizian. >From this, they construct a tubular neighborhood of thickness 2h around the surface and show that for sufficiently small h the associated tubular neighborhood mapping is bi-Lipschitzian. We prove that such surfaces are C1'1-surfaces with a bounded measurable second fundamental form. We show that the tubular neighborhood can be completely described by the algebraic distance function to ω and that it is generally not a Lipschitzian domain in R³ by providing the example of a plate around a flat surface ω verifying all their assumptions. Therefore, the G1-join of K-regular patches in the sense of Le Dret (2004) generates a new K-regular patch that is a C1'1-surface and the join is C1'1. Finally, we generalize everything to hypersurfaces generated by a bi-Lipschitzian mapping defined on a domain with facets (e.g. for sphere, torus). We also give conditions for the decomposition of a C1'1-hypersurface into C1'1-patches.
    Źródło:
    Control and Cybernetics; 2008, 37, 4; 879-911
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A sufficient condition for optimality in nondifferentiable invex programming
    Autorzy:
    Antczak, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/205838.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    funkcja półwypukła
    uogólniony gradient Clarka
    Clarke's generalized gradient
    invex function
    locally Lipschitz function
    semiconvex function
    Opis:
    In this paper sufficient optimality condition are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke's generalized gradient is used to define invexity.
    Źródło:
    Control and Cybernetics; 2001, 30, 4; 431-437
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of semilinear elliptic equation with state constraint : maximum principle for minimizing sequence, regularity, normality, sensitivity
    Autorzy:
    Sumin, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/205729.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie eliptyczne
    sensitivity
    sterowanie optymalne
    zasada maksimum
    elliptic equation
    Lipschitz continuity
    maximum principle
    minimizing sequence
    normality
    optimal control
    parametric optimal control
    pointwise state constraint
    regularity
    sequences
    value function
    Opis:
    This article deals with state constrained optimal control problem for semilinear elliptic equation in a domain Omega. The state constraint is lumped on the compactum X contained in/implied by Omega n and contains a functional parameter q in C(X ). It is shown that any minimizing approximate solution (m.a.s.) in the sense of J. Warga satisfies the pointwise maximum principle (the maximum principle for m.a.s.) if the problem is meaningful, i.e., the value of the problem is finite. It is also shown that a condition of Slater's type is sufficient for the normality in the so-called "linear-convex" problem, and the normality of the problem for some fixed value of the parameter q in C(X ) implies the Lipschitz continuity of its value function in a neighborhood of q. The paper contains illustrative examples.
    Źródło:
    Control and Cybernetics; 2000, 29, 2; 449-472
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-parametric control : uniform convergence of the optimal value functions of discretized problems
    Autorzy:
    Gugat, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206773.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    ciąg
    dyskretyzacja
    funkcja celu
    optymalizacja parametryczna
    profil momentu
    systemy sterowania minimalno-czasowe
    warunek Hoeldera
    warunek Lipschitza
    zbieżność jednakowa
    continuity
    discretization
    Hoelder condition
    Lipschitz condition
    moment problems
    optimal value function
    parametric optimization
    time-minimal control
    uniform convergence
    Opis:
    The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions fot Lipschitz and Hoelder continuity of the optimal value function of the original problem.
    Źródło:
    Control and Cybernetics; 1999, 28, 1; 7-33
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
    Autorzy:
    Baran, M.
    Pleśniak, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/1219584.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Bernstein and van der Corput-Schaake type inequalities
    semialgebraic curves
    algebraic manifolds
    pluricomplex Green function
    Lipschitz functions
    Opis:
    We show that in the class of compact, piecewise $C^1$ curves K in $ℝ^n$, the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
    Źródło:
    Studia Mathematica; 1997, 125, 1; 83-96
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lipschitz differences and Lipschitz functions
    Autorzy:
    Balcerzak, Marek
    Buczolich, Zoltán
    Laczkovich, Miklós
    Powiązania:
    https://bibliotekanauki.pl/articles/966671.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Lipschitz function
    circle group
    difference function
    Źródło:
    Colloquium Mathematicum; 1997, 72, 2; 319-324
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
    Autorzy:
    -Q. Bui, H.
    Paluszyński, M.
    Taibleson, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1287511.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Besov-Lipschitz space
    Triebel-Lizorkin space
    Littlewood-Paley function
    Calderón representation theorem
    $A_∞$ weight
    Opis:
    We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with $A_∞$ weights via a smooth kernel which satisfies "minimal" moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
    Źródło:
    Studia Mathematica; 1996, 119, 3; 219-246
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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