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    Wyświetlanie 1-12 z 12
    Tytuł:
    Optimization problems with convex epigraphs. Application to optimal control
    Autorzy:
    Kryazhimskii, A. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/908078.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie nieliniowe
    optymalizacja
    nonconvex optimization
    global optimization methods
    Opis:
    For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the "epigraph", a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear control system is described.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 4; 773-801
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A continuous-time distributed algorithm for solving a class of decomposable nonconvex quadratic programming
    Autorzy:
    Zhao, Y.
    Liu, Q.
    Powiązania:
    https://bibliotekanauki.pl/articles/91832.pdf
    Data publikacji:
    2018
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    decomposable nonconvex quadratic programming
    multi-agent network
    consensus
    Lyapunov method
    Opis:
    In this paper, a continuous-time distributed algorithm is presented to solve a class of decomposable quadratic programming problems. In the quadratic programming, even if the objective function is nonconvex, the algorithm can still perform well under an extra condition combining with the objective, constraint and coupling matrices. Inspired by recent advances in distributed optimization, the proposed continuous-time algorithm described by multi-agent network with consensus is designed and analyzed. In the network, each agent only accesses the local information of its own and from its neighbors, then all the agents in a connected network cooperatively find the optimal solution with consensus.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2018, 8, 4; 283-291
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonconvex minimization related to quadratic double-well energy - approximation by convex problemsenergy – approximation by convex problems
    Autorzy:
    Naniewicz, Z.
    Puchała, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/205686.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonconvex integrand
    minimum of convex functions
    duality
    parameterized Young measures
    Opis:
    A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied taking into account minimization of the corresponding integral functional. Such integral, as being not sequentially weakly lower semicontinuous, does not admit classical minimizers. To derive the relaxation formula for the infimum, the appropriate minimizing sequence is constructed. It consists of solutions of some approximating convex problems involving characteristic functions related to the phase energies. The weak limit of this sequence and the weak limit of the sequence of solutions of dual problems combined with the weak-star limits of the characteristic functions related to the phase energies allow to establish the final relaxation formula. It is also shown that infimum can be expressed by the Young measure associated with constructed minimizing sequence. An explicit form of Young measure in some regions of the involved domain is calculated.
    Źródło:
    Control and Cybernetics; 2012, 41, 3; 525-543
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Software Platform for Global Optimization
    Autorzy:
    Niewiadomska-Szynkiewicz, E.
    Marks, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/308471.pdf
    Data publikacji:
    2010
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    global optimization
    integrated software systems
    nonconvex optimization
    numerical libraries
    price management
    Opis:
    This paper addresses issues associated with the global optimization algorithms, which are methods to find optimal solutions for given problems. It focuses on an integrated software environment - global optimization object-oriented library (GOOL), which provides the graphical user interface together with the library of solvers for convex and nonconvex, unconstrained and constrained problems. We describe the design, performance and possible applications of the GOOL system. The practical example - price management problem - is provided to illustrate the effectiveness and range of applications of our software tool.
    Źródło:
    Journal of Telecommunications and Information Technology; 2010, 3; 49-56
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory
    Autorzy:
    Djebali, Smaïl
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/729271.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusions
    boundary value problem
    fixed point
    compact
    convex
    nonconvex
    decomposable
    continuous selection
    controllability
    Opis:
    In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 23-49
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalizing trade-off deirections in multiobjective optimization
    Autorzy:
    Mäkelä, M. M.
    Nikulin, Y.
    Mezei, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205690.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    generalized trade-off directions
    multiobjective optimization
    geometrical characterization
    convex and nonconvex optimization
    optimality principles
    Opis:
    We consider a general multiobjective optimization problem with five basic optimality principles: efficiency, weak and proper Pareto optimality, strong efficiency and lexicographic optimality. We generalize the concept of trade-off directions defining them as some optimal surface of appropriate cones. In convex optimization, the contingent cone can be used for all optimality principles except lexicographic optimality, where the cone of feasible directions is useful. In nonconvex case the contingent cone and the cone of locally feasible directions with lexicographic optimality are helpful. We derive necessary and sufficient geometrical optima lity conditions in terms of corresponding trade-off directions for both convex and nonconvex cases.
    Źródło:
    Control and Cybernetics; 2012, 41, 3; 561-576
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Augmented lagrangian methods for a class of convex and nonconvex contact problems
    Autorzy:
    Telega, J. J.
    Gałka, A.
    Bielski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/279910.pdf
    Data publikacji:
    2001
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    unilateral contact problems without friction
    plates
    Koiter's shell model
    augmented Lagrangian methods
    nonconvex duality
    Opis:
    The aim of this contribution is threefold. First, we formulate unilateral contact problems for three models of plates and the Koiter shell model. Contact conditions have been formulated on the face being in contact with an obstacle and not on the mid-plane of the plate or the middle surface of the shell. Such a rigorous approach results in nonconvex minimization problems even in the case of thin, geometrically linear plates. Existence theorems are formulated for each model considered. Second, the Ito and Kunisch (1990, 1995) augmented Lagrangians methods have been extended to nonconvex problems. Third, nonconvex duality theory by Rockafellar and Wets (1998), valid for finite-degree-of-freedom systems has been extended to continuous systems. Specific examples have also been provided.
    Metody rozszerzonego lagranżianu dla pewnej klasy wypukłych i niewypukłych zagadnień kontaktowych. Cel pracy jest trojaki. Po pierwsze, sformułowane zostały jednostronne zagadnienia kontaktowe dla trzech modeli płyt oraz liniowego modelu powłok Koitera. Warunki kontaktu zostały sformułowane na powierzchni będące w kontakcie z podłożem, a nie na powierzchni środkowej płyty lub powłoki. Takie ścisłe podejście prowadzi do niewypukłych zadań minimalizacji, nawet w przypadku płyt cienkich. Dla każdego zagadnienia sformułowano twierdzenie o istnieniu rozwiązań. Po drugie, metody rozszerzonego lagranżianu Ito i Kunischa (1990, 1995) uogólnione zostały na przypadek zagadnień niewypukłych. Po trzecie, teoria dualności Rockafellara i Wetsa (1998), opracowana dla skończenie wymiarowych zagadnień niewypukłych, została rozszerzona na przypadek układów ciągłych. Podano również kilka przykładów.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2001, 39, 3; 741-768
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Localization in Wireless Sensor Networks Using Heuristic Optimization Techniques
    Autorzy:
    Niewiadomska-Szynkiewicz, E.
    Marks, M.
    Kamola, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/308429.pdf
    Data publikacji:
    2011
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    evolutionary strategy
    genetic algorithm
    localization
    location systems
    nonconvex optimization
    simulated annealing
    wireless sensor network
    Opis:
    Many applications of wireless sensor networks (WSN) require information about the geographic location of each sensor node. Devices that form WSN are expected to be remotely deployed in large numbers in a sensing field, and to self-organize to perform sensing and acting task. The goal of localization is to assign geographic coordinates to each device with unknown position in the deployment area. Recently, the popular strategy is to apply optimization algorithms to solve the localization problem. In this paper, we address issues associated with the application of heuristic techniques to accurate localization of nodes in a WSN system. We survey and discuss the location systems based on simulated annealing, genetic algorithms and evolutionary strategies. Finally, we describe and evaluate our methods that combine trilateration and heuristic optimization.
    Źródło:
    Journal of Telecommunications and Information Technology; 2011, 4; 55-64
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization
    Autorzy:
    El Mouatasim, A.
    Ellaia, R.
    Souza de Cursi, J. E.
    Powiązania:
    https://bibliotekanauki.pl/articles/908374.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja
    zaburzenie stochastyczne
    zaburzenie losowe
    nonconvex optimization
    stochastic perturbation
    variable metric method
    nonsmooth optimization
    generalized gradient
    Opis:
    We consider the global optimization of a nonsmooth (nondifferentiable) nonconvex real function. We introduce a variable metric descent method adapted to nonsmooth situations, which is modified by the incorporation of suitable random perturbations. Convergence to a global minimum is established and a simple method for the generation of suitable perturbations is introduced. An algorithm is proposed and numerical results are presented, showing that the method is computationally effective and stable.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 4; 463-474
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A single image deblurring approach based on a fractional order dark channel prior
    Autorzy:
    Yu, Xiaoyuan
    Xie, Wei
    Yu, Jinwei
    Powiązania:
    https://bibliotekanauki.pl/articles/2172119.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    blind image deblurring
    fractional order dark channel prior
    nonconvex problem
    obraz rozmyty
    rząd ułamkowy
    problem niewypukły
    Opis:
    The dark channel prior has been successfully applied to solve the blind deblurring problem on different scene images. Since the dark channel of the blurry-noise image is similar to that of the corresponding clear image, the sparsity of the dark channel is less effective for image blind deblurring. Inspired by the fact that a fractional order calculation can inhibit the noise and preserve the texture information of the image, a fractional order dark channel prior is proposed for image deblurring in this paper. It is appropriate for kernel estimation where input images and intermediate images are processed by using a fractional order dark channel prior. Furthermore, the non-convex problem is solved by the half-quadratic splitting method, and some metrics are used for deblurring image quality assessment. Finally, quantitative and qualitative experimental results show that the proposed method achieves state-of-the-art results on synthetic and real blurry images.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2022, 32, 3; 441--454
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear multivalued boundary value problems
    Autorzy:
    Bader, Ralf
    Papageorgiou, Nikolaos
    Powiązania:
    https://bibliotekanauki.pl/articles/729304.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    usc and lsc multifunction
    measurable selection
    Leray-Schauder alternative theorem
    Sobolev space
    compact embedding
    maximal monotone map
    coercive map
    surjective map
    convex and nonconvex problem
    nonlinear boundary conditions
    Opis:
    In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 127-148
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
    Autorzy:
    Barboteu, M.
    Bartosz, K.
    Kalita, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/330898.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    linearly elastic material
    bilateral contact
    nonmonotone friction law
    hemivariational inequality
    finite element method
    error estimate
    nonconvex proximal bundle method
    quasi augmented Lagrangian method
    Newton method
    metoda elementów skończonych
    szacowanie błędu
    metoda Lagrangiana
    metoda Newtona
    Opis:
    We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 263-276
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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