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    Wyświetlanie 1-4 z 4
    Tytuł:
    Automatic Differentiation in the Optimization of Imaging Optical Systems
    Autorzy:
    Werner, Jürgen
    Hillenbrand, Matthias
    Hoffmann, Armin
    Sinzinger, Stefan
    Powiązania:
    https://bibliotekanauki.pl/articles/1373549.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    automatic differentiation
    optimization
    lens design
    Opis:
    Automatic differentiation is an often superior alternative to numerical differentiation that is yet unregarded for calculating derivatives in the optimization of imaging optical systems. We show that it is between 8% and 34% faster than numerical differentiation with central difference when optimizing various optical systems.
    Źródło:
    Schedae Informaticae; 2012, 21; 169-175
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Efficient calculation of sensitivities for optimization problems
    Autorzy:
    Kowarz, Andreas
    Walther, Andrea
    Powiązania:
    https://bibliotekanauki.pl/articles/729449.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    automatic differentiation
    sensitivities
    forward mode
    Opis:
    Sensitivity information is required by numerous applications such as, for example, optimization algorithms, parameter estimations or real time control. Sensitivities can be computed with working accuracy using the forward mode of automatic differentiation (AD).
    ADOL-C is an AD-tool for programs written in C or C++. Originally, when applying ADOL-C, tapes for values, operations and locations are written during the function evaluation to generate an internal function representation. Subsequently, these tapes are evaluated to compute the derivatives, sparsity patterns etc., using the forward or reverse mode of AD. The generation of the tapes can be completely avoided by applying the recently implemented tapeless variant of the forward mode for scalar and vector calculations. The tapeless forward mode enables the joint computation of function and derivative values directly from main memory within one sweep. Compared to the original approach shorter runtimes are achieved due to the avoidance of tape handling and a more effective, joint optimization for function and derivative code.
    Advantages and disadvantages of the tapeless forward mode provided by ADOL-C will be discussed. Furthermore, runtime comparisons for two implemented variants of the tapeless forward mode are presented. The results are based on two numerical examples that require the computation of sensitivity information.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 119-134
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Foundational Certification of Code Transformations Using Automatic Differentiation
    Autorzy:
    Tadjouddine, E. M.
    Lv, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/305770.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    relational Hoare logic
    abductive reasoning
    certification
    automatic differentiation
    Opis:
    Automatic Differentiation (AD) is concerned with the semantics augmentation of an input program representing a function to form a transformed program that computes the function’s derivatives. To ensure the correctness of the AD transformed code (particularly for safety-critical applications), we aim at certifying the algebraic manipulations at the heart of the AD process. We have considered a WHILE-language, and have shown how such proofs can be constructed by using appropriate relational Hoare logic. In particular, we have shown how such inference rules can be constructed for both the forward- and reverse-mode AD by using an abductive logical reasoning.
    Źródło:
    Computer Science; 2014, 15 (2); 215-236
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
      Wyświetlanie 1-4 z 4

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