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    Wyświetlanie 1-5 z 5
    Tytuł:
    Object library of algorithms for dynamic optimization problems; Benchmarking SQP and nonlinear interior point methods
    Autorzy:
    Błaszczyk, J.
    Karbowski, A.
    Malinowski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/929795.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja dynamiczna
    programowanie kwadratowe sekwencyjne
    różniczkowanie automatyczne
    obliczenia numeryczne
    analiza danych
    dynamic optimization
    large-scale optimization
    sequential quadratic programming
    nonlinear interior-point methods
    object-oriented numerical computations
    automatic differentiation
    performance data analysis
    Opis:
    The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 515-537
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tikhonov regularization and constrained quadratic programming for magnetic coil design problems
    Autorzy:
    Garda, B.
    Galias, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/330150.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    coil design problem
    constrained quadratic programming
    Tikhonov regularization
    projektowanie cewki
    programowanie kwadratowe
    regularyzacja Tikhonova
    Opis:
    In this work, the problem of coil design is studied. It is assumed that the structure of the coil is known (i.e., the positions of simple circular coils are fixed) and the problem is to find current distribution to obtain the required magnetic field in a given region. The unconstrained version of the problem (arbitrary currents are allowed) can be formulated as a Least-SQuares (LSQ) problem. However, the results obtained by solving the LSQ problem are usually useless from the application point of view. Moreover, for higher dimensions the problem is ill-conditioned. To overcome these difficulties, a regularization term is sometimes added to the cost function, in order to make the solution smoother. The regularization technique, however, produces suboptimal solutions. In this work, we propose to solve the problem under study using the constrained Quadratic Programming (QP) method. The methods are compared in terms of the quality of the magnetic field obtained, and the power of the designed coil. Several 1D and 2D examples are considered. It is shown that for the same value of the maximum current the QP method provides solutions with a higher quality magnetic field than the regularization method.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 249-257
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A family of model predictive control algorithms with artificial neural networks
    Autorzy:
    Ławryńczuk, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/929631.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie predykcyjne
    sieć neuronowa
    optymalizacja
    linearyzacja
    programowanie kwadratowe
    predictive control
    neural networks
    optimisation
    linearisation
    quadratic programming
    Opis:
    This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used on-line to determine local linearisation and a nonlinear free trajectory. Single-point and multi-point linearisation methods are discussed. The MPC-NPL structure is far more reliable and less computationally demanding in comparison with the MPC-NO one because it solves a quadratic programming problem, which can be done efficiently within a foreseeable time frame. At the same time, closed-loop performance of both algorithm classes is similar. Finally, a hybrid MPC algorithm with Nonlinear Prediction, Linearisation and Nonlinear optimisation (MPC-NPL-NO) is discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 2; 217-232
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An infinite horizon predictive control algorithm based on multivariable input-output models
    Autorzy:
    Ławryńczuk, M.
    Tatjewski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/907410.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie predykcyjne
    horyzont nieskończony
    programowanie kwadratowe
    model predictive control
    stability
    infinite horizon
    singular value decomposition
    quadratic programming
    Opis:
    In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 2; 167-180
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An SQP trust region method for solving the discrete-time linear quadratic control problem
    Autorzy:
    Mostafa, E. M. E.
    Powiązania:
    https://bibliotekanauki.pl/articles/331409.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    programowanie sekwencyjne
    programowanie kwadratowe
    system dyskretno-czasowy
    output feedback control design
    sequential quadratic programming
    trust region method
    Opis:
    In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution to initiate the proposed SQP trust region method. To demonstrate the effectiveness of the method, some numerical results are presented in detail.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 353-363
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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