Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "cones" wg kryterium: Temat

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-4 z 4
    Tytuł:
    Second-order optimality conditions in nonsmooth vector optimization
    Autorzy:
    Yadav, Priyanka
    Powiązania:
    https://bibliotekanauki.pl/articles/31342762.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    vector optimization
    cones
    nonsmooth second-order cone-convexity
    second-order optimality
    duality
    Opis:
    In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.
    Źródło:
    Control and Cybernetics; 2023, 52, 1; 35-51
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimality conditions for a class of relaxed quasiconvex minimax problems
    Autorzy:
    Diem, H. T. H.
    Khanh, P. Q.
    Powiązania:
    https://bibliotekanauki.pl/articles/205919.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    minimax problem
    optimality conditions
    convex sublevel sets
    normal cones
    star subdifferentials
    adjusted subdiffer- entials
    Opis:
    A class of minimax problems is considered. We approach it with the techniques of quasiconvex optimization, which includes most important nonsmooth and relaxed convex problems and has been intensively developed. Observing that there have been many contributions to various themes of minimax problems, but surprisingly very few on optimality conditions, the most traditional and developed topic in optimization, we establish both necessary and sufficient conditions for solutions and unique solutions. A main feature of this work is that the involved functions are relaxed quasi- convex in the sense that the sublevel sets need to be convex only at the considered point. We use star subdifferentials, which are slightly bigger than other subdifferentials applied in many existing results for minimization problems, but may be empty or too small in various situations. Hence, when applied to the special case of minimization problems, our results may be more suitable. Many examples are provided to illustrate the applications of the results and also to discuss the imposed assumptions.
    Źródło:
    Control and Cybernetics; 2014, 43, 2; 249-260
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equivalence of second order optimality conditions for bang-bang control problems. Part 2 : Proofs, variational derivatives and representations
    Autorzy:
    Osmolovskii, N. P.
    Maurer, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/969736.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    bang-bang control
    second order necessary and sufficient conditions
    critical cones
    equivalence of quadratic forms
    representation of the Hessian of the Lagrangian
    Opis:
    In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit relations between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and initial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms.
    Źródło:
    Control and Cybernetics; 2007, 36, 1; 5-45
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Towards historical roots of necessary conditions of optimality: Regula of Peano
    Autorzy:
    Dolecki, S.
    Greco, G. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/970285.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    różniczkowalność
    zbiór wypukły
    differentiability
    convex set
    Kuratowski limit of sets
    tangent cones
    condition of optimality
    mean value theorem
    Peano remainder
    Peano's regula
    strict derivability
    Peano's Formulario Mathematico
    Peano's Geometric Calculus
    Grassmann's Ausdehnungslehre
    Opis:
    At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The theorem on necessary conditions of optimality (Regula) is one of these. The formal language of logic that he developed, enabled him to perceive mathematics with great precision and depth. Actually he built mathematics axiomatically based exclusively on logical and set-theoretic primitive terms and properties, which was a revolutionary turning point in the development of mathematics.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 491-518
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies