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    Wyświetlanie 1-8 z 8
    Tytuł:
    Optimality conditions in set-valued optimization using approximations as generalized derivatives
    Autorzy:
    Gadhi, Nazih Abderrazzak
    Ichatouhane, Aissam
    Powiązania:
    https://bibliotekanauki.pl/articles/31342744.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    approximations
    set-valued optimization
    local weak l-minimal solutions
    optimality conditions
    Opis:
    The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.
    Źródło:
    Control and Cybernetics; 2022, 51, 4; 425-444
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error analysis of discrete approximations to bang-bang optimal control problems: the linear case
    Autorzy:
    Veliov, V. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970563.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    liniowy system sterowania
    aproksymacja dyskretna
    szacowanie błędów
    linear control systems
    discrete approximations
    error estimates
    Opis:
    The paper presents an error estimate for Runge-Kutta direct discretizations of terminal optimal control problems for linear systems. The optimal control for such problems is typically discontinuous, and Lipschitz stability of the solution with respect to perturbations does not necessarily hold. The estimate (in terms of the optimal controls) is of first order if certain recently obtained sufficient conditions for structural stability hold, and of fractional order, otherwise. The main tool in the proof is the established relation between the local convexity index of the reachable set and the multiplicity of zeros of appropriate switching functions associated with the problem.
    Źródło:
    Control and Cybernetics; 2005, 34, 3; 967-982
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local cone approximations in optimization
    Autorzy:
    Castellani, M.
    Pappalardo, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970281.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonsmooth optimization
    cone approximations
    generalized directional epiderivatives
    optimality conditions
    constraint qualifications
    mean value theorem
    error bound
    Opis:
    We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 583-600
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical experiments with model equations of cancer invasion of tissue
    Autorzy:
    Kolev, M.
    Zubik-Kowal, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/206179.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    in vivo tumorigenicity
    cancer cells
    proliferation
    chemotaxis
    haptotaxis
    extracellular matrix
    tumour invasion
    mathematical model
    animal models
    approximations
    Opis:
    In this paper we investigate a mathematical model of cancer invasion of tissue, which incorporates haptotaxis, chemotaxis, proliferation and degradation rates for cancer cells and the extracellular matrix, kinetics of urokinase receptor, and urokinase plasminogen activator cycle. We solve the model using spectrally accurate approximations and compare its numerical solutions with laboratory data. The spectral accuracy allows to use low-dimensional matrices and vectors, which speeds up the computations of the numerical solutions and thus to estimate the parameter values for the model equations. Our numerical results demonstrate correlations between numerical data computed from the mathematical model and in vivo tumour growth rates from prostate cell lines.
    Źródło:
    Control and Cybernetics; 2011, 40, 3; 779-791
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An improved comparison of three rough set approaches to missing attribute values
    Autorzy:
    Grzymala-Busse, J. W.
    Grzymala-Busse, W. J.
    Hippe, Z. S.
    Rząsa, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/969797.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    incomplete data sets
    missing attribute values
    approximations for incomplete data
    LERS data mining system
    MLEM2 algorithm
    Opis:
    In a previous paper three types of missing attribute values: lost values, attribute-concept values and "do not care" conditions were compared using six data sets. Since previous experimental results were affected by large variances due to conducting experiments on different versions of a given data set, we conducted new experiments, using the same pattern of missing attribute values for all three types of missing attribute values and for both certain and possible rules. Additionally, in our new experiments, the process of incremental replacing specified values by missing attribute values was terminated when entire rows of the data sets were full of missing attribute values. Finally, we created new, incomplete data sets by replacing the specified values starting from 5% of all attribute values, instead of 10% as in the previous experiments, with an increment of 5% instead of the previous increment of 10%. As a result, it is becoming more clear that the best approach to missing attribute values is based on lost values, with small difference between certain and possible rules, and that the worst approach is based on "do not care" conditions, certain rules. With our improved experimental setup it is also more clear that for a given data set the type of the missing attribute values should be selected individually.
    Źródło:
    Control and Cybernetics; 2010, 39, 2; 469-486
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of semilinear evolution inclusions via discrete approximations
    Autorzy:
    Mordukhovich, B. S.
    Wang, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839178.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    analiza wariacyjna
    różniczkowanie uogólnione
    aproksymacja dyskretna
    warunek konieczny optymalności
    optimal control
    variational analysis
    generalized differentiation
    semilinear evolution inclusions
    discrete approximations
    necessary optimality conditions
    Opis:
    This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
    Źródło:
    Control and Cybernetics; 2005, 34, 3; 849-870
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
    Autorzy:
    Mordukhovich, B. S.
    Wang, D.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/969562.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    discrete approximations
    optimal control
    variational analysis
    endpoint constraints
    delay-differential inclusions
    multivalued initial conditions
    extended Euler-Lagrange formalism
    generalized differentiation
    Banach and Asplund spaces
    necessary optimality conditions
    Opis:
    This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 393-428
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of constrained delay-differential inclusions with multivalued initial conditions
    Autorzy:
    Mordukhovich, B. S.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970519.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja dyskretna
    warunek konieczny optymalności
    analiza wariacyjna
    stabilność
    optymalizacja niegładka
    różniczkowanie uogólnione
    delay-differential inclusions
    discrete approximations
    necessary optimality conditions
    variational analysis
    stability
    nonsmooth optimization
    generalized differentiation
    Opis:
    This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 585-609
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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