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    Wyświetlanie 1-9 z 9
    Tytuł:
    Regularization and discretization of linear-quadratic control problems
    Autorzy:
    Alt, W.
    Seydenschwanz, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206162.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    bang-bang control
    regularization
    discretization
    Opis:
    We analyze regularizations of a class of linear-quadratic optimal control problems with control appearing linearly. It is shown that if the optimal control is bang-bang or if a coercivity condition for the state variables is satisfied, the solutions are continuous functions of the regularization parameter. Combining error estimates for Euler discretizations of the regularized problems with those for the regularization error, we choose the regularization parameter in dependence of the meshsize to obtain optimal convergence rates for the discrete solutions. Numerical experiments confirm the theoretical findings.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 903-920
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints
    Autorzy:
    Neitzel, I.
    Troltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/970314.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    semilinear parabolic equation
    pointwise state constraints
    Moreau-Yosida regularization
    Lavrentiev regularization
    convergence
    strong regularity
    local uniqueness
    Opis:
    Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.
    Źródło:
    Control and Cybernetics; 2008, 37, 4; 1013-1043
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On solvability of boundary value problems in elastoplasticity
    Autorzy:
    Chludnev, A.
    Sokołowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205983.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    elastoplastyczność
    pękanie
    zagadnienie brzegowe
    boundary problem
    cracks
    elastoplasticity
    penalty
    regularization
    Opis:
    In the paper the existence of a solution to the thress-dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is established. The proof is based on a suitable combination of the parabolic regularization of equations and the penalty method for the elastoplastic yield condition. The method is applied in the case of the domain with smooth boundary as well as in the case of an interior crack. It is shown that the weak solutions to the elastoplastic problem satisfying the variational inequality meet all boundary conditions.
    Źródło:
    Control and Cybernetics; 1998, 27, 2; 311-330
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the regularization error of state constrained Neumann control problems
    Autorzy:
    Krumbiegel, K.
    Rosch, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/969594.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    elliptic equation
    state constraints
    boundary control
    regularization
    virtual control
    Opis:
    A linear elliptic optimal control problem with point-wise state constraints in the interior of the domain is considered. Furthermore, the control is given on the boundary with associated constraints. An artificial distributed control is introduced in the cost functional, in the state equation and in the state constraints. Since there are no control constraints for the artificial control, efficient numerical methods can be easily established. Based on a possible violation of the pure pointwise state constraints, an error estimate for the regularization error is derived. The theoretical results are illustrated by numerical tests.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 369-392
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints
    Autorzy:
    Wachsmuth, D.
    Wachsmuth, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/206129.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    source condition
    discrepancy principle
    nonsmooth optimization
    convex constraints
    sparsity
    regularization error estimates
    Opis:
    In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive a-priori regularization error estimates if the regularization parameter as well as the noise level tend to zero. We rely on an assumption that is a combination of a source condition and of a structural assumption on the active sets. Moreover, we introduce a strategy to choose the regularization parameter in dependence of the noise level. We prove convergence of this parameter choice rule with optimal order.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 1125-1158
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimizing properties of an inertial dynamical system with geometric damping : link with proximal methods
    Autorzy:
    Attouch, H.
    Bolte, J.
    Redont, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/205719.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dynamical systems in optimization
    entropic methods in optimization
    proximal regularization method
    steepest descent method
    Opis:
    The second-order dynamical system x + [alpha]x + Beta[...] = 0, alpha > 0, Beta > 0, where the Hessian [...]Phi(x) acts as a geometric damping, is introduced, mainly in view of the minimization of [Phi]. Minimizing [Phi] is a problem equivalent to the minimization of the functional [Psi]a,b(x, y) = 1/b^2Phi(x) + 1/2|ax + by|^2, a > 0, b > 0. The latter naturallv appears in the proximal regularization of Phi ; it may also be viewed as an energy. The continuous steepest descent method applied to [Psi]a,b yields a first-order system, which proves to he equivalent to the above-mentioned second-order system, when [Phi] is of class [C^2].
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 643-657
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regularization of non-coercive quasi variational inequalities
    Autorzy:
    Giannessi, F.
    Khan, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/205586.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    operator monotoniczny i pseudomonotoniczny
    zbieżność
    convergence
    monotone and pseudo-monotone operators
    non-coercive
    quasi-variational inequalities
    regularization
    Opis:
    This paper is devoted to the regularization of quasi-variational inequalities. The quasi-variational inequality is considered with multivalued operator. The operator involved is taken to be non-coercive and the data are assumed to be known approximately only. Under the assumption that the quasi-variational inequality be solvable, a weakly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method.
    Źródło:
    Control and Cybernetics; 2000, 29, 1; 91-110
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    φ-regular functions in Asplund spaces
    Autorzy:
    Ngai, H. V.
    Thera, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970242.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    φ-regularity
    Frechet subdifferential
    limiting sub-differential
    prox-regularity
    lower-C2 function
    convexly composite function
    Moreau envelope
    regularization
    Opis:
    We introduce in the context of Asplund spaces, a new class of (φ-regular functions. This new concept generalizes the one of prox-regularity introduced by Poliquin & Rockafellar (2000) in Rn and extended to Banach spaces by Bernard & Thibault (2004). In particular, the class of φ-regular functions includes all lower semi-continuous convex functions, all lower-C2 functions, and convexly C1,0-composite functions as well. Geometrical and subdifferential characterizations for this new class of functions are investigated.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 755-774
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Proximal-based regularization methods and successive approximation of variational inequalities in Hilbert spaces
    Autorzy:
    Kaplan, A.
    Tichatschke, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/205832.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    funkcja Bregmana
    metoda punktów proksymalnych
    nierówność wariacyjna
    operator monotoniczny
    regularyzacja
    Bregman function
    monotone operators
    proximal point methods
    regularization
    variational inequalities
    Opis:
    For variational inequalities with multi-valued, maximal monotone operators in Hilbert spaces we study proximal-based methods with an improvement of the data approximation after each (approximately performed) proximal iteration. The standard conditions on a distance functional of Bregman's type are weakened, depending on a "reserve of monotonicity" of the operator in the variational inequality, and the enlargement concept is used for approximating the operator. Weak convergence of the proxinnal iterates to a solution of tire original problem is proved. The construction of the [epsilon]-enlargement of monotone operators is analyzed for some particular cases.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 521-544
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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