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    Wyświetlanie 1-9 z 9
    Tytuł:
    Optimal control of partial differential equations with affine control constraints
    Autorzy:
    Reyes, J. R. de los
    Kunisch, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839187.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    affine control constraints
    semi-smooth Newton methods
    Opis:
    Numerical solution of PDE optimal control problems involving affine pointwise control constraints is investigated. Optimality conditions are derived and a semi-smooth Newton method is presented. Global and local superlinear convergence of the method are obtained for linear problems. Differently from box constraints, in the case of general affine constraints a proper weighting of the control costs is essential for superlinear convergence of semi-smooth Newton methods. This is also demonstrated numerically by controlling the two-dimensional Stokes equations with different kinds of affine constraints.
    Źródło:
    Control and Cybernetics; 2009, 38, 4A; 1217-1249
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-dimensional Newtons problem of minimal resistance
    Autorzy:
    Silva, C. J.
    Torres, D. F.
    Powiązania:
    https://bibliotekanauki.pl/articles/969988.pdf
    Data publikacji:
    2006
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Newton's problem of minimal resistance
    dimension two
    calculus of variations
    optimal control
    Opis:
    Newton's problem of minimal resistance is one of the first problems of optimal control: it was proposed, and its solution given, by Isaac Newton in his masterful Principia Mathematica, in 1686. The problem consists of determining, in dimension three, the shape of an axis-symmetric body, with assigned radius and height, which offers minimum resistance when it is moving in a resistant medium. The problem has a very rich history and is well documented in the literature. Of course, at a first glance, one suspects that the two dimensional case should be well known. Nevertheless, we have looked into numerous references and asked at least as many experts on the problem, and we have not been able to identify a single source. Solution was always plausible to everyone who thought about the problem, and writing it down was always thought not to be worthwhile. Here we show that this is not the case: the two-dimensional problem is richer than the classical one, being, in some sense, more interesting. Novelties include: (i) while in the classical three-dimensional problem only the restricted case makes sense (without restriction on the monotonicity of admissible functions the problem does not admit a local minimum), we prove that in dimension two the unrestricted problem is also well-posed when the ratio of height versus radius of base is greater than a given quantity; (ii) while in three dimensions the (restricted) problem has a unique solution, we show that in the restricted two-dimensional problem the minimizer is not always unique - when the height of the body is less or equal than its base radius, there exists infinitely many minimizing functions.
    Źródło:
    Control and Cybernetics; 2006, 35, 4; 965-975
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A logarithmic barrier function method for solving nonlinear multiobjective programming problems
    Autorzy:
    Tlas, M.
    Abdul Ghani, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/970097.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    metoda wewnętrzna
    metoda Newtona
    multiobjective programming
    interior methods
    Newton method
    barrier functions
    Opis:
    An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R^n, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton method for determining Newton's directions along which line searches are performed. It also has been proved that the number of iterations required by the suggested algorithm to converge to an [epsilon]-optimal solution is 0(m|ln[epsilon]|), depending on predetermined error tolerance [epsilon] and the number of constraints m.
    Źródło:
    Control and Cybernetics; 2005, 34, 2; 487-504
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Adaptive Newton-like method for shape optimization
    Autorzy:
    Roche, J. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/970159.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optymalizacja kształtu
    zdolność przystosowania się
    shape optimization
    Newton-like algorithm
    posteriori error
    adaptability
    Opis:
    The aim of this work is to introduce an adaptive strategy to monitor the rate of convergence of a Newton-like method in numerical shape optimization. Such superlinear iterative algorithms are often computationally intensive and the rate of convergence depends on how accurate the numerical solution of the state equation is. The model concerns a cost function depending on the unknown domain [Omega], and the solution of an integral equation.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 363-377
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximation of optimal control problems with bound constraints by control parameterization
    Autorzy:
    Alt, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/970516.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne nieliniowe
    metoda Newtona
    nonlinear optimal control
    bound constraints
    Newton's method
    control parameterization
    Opis:
    We consider nonlinear optimal control problems with bound constraints for the controls. Under the assumption that the optimal control is continuous and has finitely many smooth boundary arcs, we show that the system of optimahty conditions can be reduced to a system of operator equations. Based on this system we investigate convergence of approximations by control parameterization.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 451-472
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Metric regularity under approximations
    Autorzy:
    Dontchev, A. L.
    Veliov, V. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970750.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    metric regularity
    inexact iterative methods
    Newton method
    proximal point method
    discrete approximation
    optimal control
    Opis:
    In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approximations in optimal control.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1283-1303
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A regularized Newton method in electrical impedance tomography using shape Hessian information
    Autorzy:
    Eppler, K.
    Harbrecht, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/970140.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    tomografia impedancyjna
    optymalizacja kształtu
    brzegowe równanie całkowe
    electrical impedance tomography
    shape optimization
    boundary integral equation
    Newton type descent
    Opis:
    The present paper is concerned with the identification of an obstacle or void of different conductivity included in a two-dimensional domain by measurements of voltage and currents at the boundary. We employ a reformulation of the given identification problem as a shape optimization problem as proposed by Roche and Sokolowski (1996). It turns out that the shape Hessian degenerates at the given hole which gives a further hint on the ill-posedness of the problem. For numerical methods, we propose a preprocessing for detecting the barycentre and a crude approximation of the void or hole. Then, we resolve the shape of the hole by a regularized Newton method.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 203-225
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation
    Autorzy:
    Heinkenschloss, M.
    Troeltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/206519.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równania paraboliczne
    równania różniczkowe
    stabilność
    sterowanie optymalne
    control constraints
    Lagrange-SQP-Newton method
    optimal control
    phase field equation
    programming method
    sequential quadratic
    Opis:
    This paper investigates the local convergence of the Lagrange-SQP-Newton method applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof convergence of the controls with respect to the L[sup 2](Q) norm and with respect to the L[sup infinity](Q) norm.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 177-211
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fast level set based algorithms using shape and topological sensitivity information
    Autorzy:
    Hintermuller, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970129.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    algorytm opadania
    metoda Newtona
    analiza wrażliwości
    optymalizacja kształtu
    optymalizacja topologiczna
    descent algorithm
    level set method
    Newton method
    sensitivity analysis
    shape optimization
    topology optimization
    Opis:
    A framework for descent algorithms using shape as well as topological sensitivity information is introduced. The concept of gradient-related descent velocities in shape optimization is defined, a corresponding algorithmic approach is developed, and a convergence analysis is provided. It is shown that for a particular choice of the bilinear form involved in the definition of gradient-related directions a shape Newton method can be obtain. The level set methodology is used for representing and updating the geometry during the iterations. In order to include topological changes in addition to merging and splitting of existing geometries, a descent algorithm based on topological sensitivity is proposed. The overall method utilizes the shape sensitivity and topological sensitivity based methods in a serial fashion. Finally, numerical results are presented.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 305-324
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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