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Wyszukujesz frazę "sufficient conditions for optimality" wg kryterium: Temat

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    Wyświetlanie 1-4 z 4
    Tytuł:
    On localizing global Pareto solutions in a given convex set
    Autorzy:
    Drwalewska, Agnieszka
    Gajek, Lesław
    Powiązania:
    https://bibliotekanauki.pl/articles/1338686.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    sufficient and necessary conditions for optimality
    Pareto optimal solutions
    dual cones
    feasible directions
    Opis:
    Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect to the cone generating the preference relation.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 4; 383-394
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy
    Autorzy:
    Świerniak, A.
    Ledzewicz, U.
    Schättler, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/908158.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    medycyna
    matematyka
    compartmental models
    cancer chemotherapy
    optimal control
    necessary and sufficient conditions for optimality
    Opis:
    We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 357-368
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
    Autorzy:
    Leszczynski, M.
    Ratajczyk, E.
    Ledzewicz, U.
    Schättler, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/255130.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    optimal control
    sufficient conditions for optimality
    method of characteristics
    pharmacodynamic model
    Opis:
    We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
    Źródło:
    Opuscula Mathematica; 2017, 37, 3; 403-419
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of pandemic with game methodology and numerical approximation
    Autorzy:
    Matusik, Radosław
    Nowakowski, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/29432416.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    COVID-19
    game model of pandemic
    approximate dual dynamic programming
    sufficient approximate optimality conditions for Nash equilibrium
    numerical algorithm
    Opis:
    We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.
    Źródło:
    Archives of Control Sciences; 2023, 33, 3; 651--680
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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