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    Wyświetlanie 1-9 z 9
    Tytuł:
    A Proximal Bundle Method with Approximate Subgradient Linearizations
    Raport Badawczy = Research Report ; RB/65/2004
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    18 pages ; 21 cm
    The paper presents a proximal bundle method for minimizing a convex function f over a closed convex set. It only requires evaluating f and its subgradients with an accuracy e > 0, which is fixed but possibly unknown. It asymptotically finds points that are e-optimal. When applied to Lagrangian relaxation, it allows for e-accurate solutions of Lagrangian subproblems, and finds e-optimal solutions of convex programs.
    Bibliography p. 17-18
    18 stron ; 21 cm
    Bibliografia s. 17-18
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/58/2006
    A Method of Centers with Approximate Subgradient Linearizations for Nonsmooth Convex Optimization
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliography p. 24
    24 stron ; 21 cm
    24 pages ; 21 cm
    The paper presents a proximal bundle method for constrained convex optimization. It only requires evaluating the problem functions and their subgradients with an unknown accuracy epsilon. Employing a combination of the classic method of centers improvement function with an exact penalty function, it does not need a feasible starting point. It asymptotically finds points with at least ε-optimal objective values that are ε- feasible. When applied to the solution of LP programs via column generation, it allows for ε-accurate solutions of column generation subproblems.
    Bibliografia s. 24
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Bundle methods for convex minimization with partially inexact oracles
    Raport Badawczy = Research Report ; RB/36/2009
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. 25-28
    28 stron ; 21 cm
    28 pages ; 21 cm
    Recently the proximal bundle method for minimizing a convex function has been extended to an inexact oracle that delivers function and subgradient values of unknown accuracy. This method has been adapted to a partially inexact oracle that becomes exact only when an objective target level for a descent step is met. In Lagrangian relaxation, such oracles may save work by evaluating the dual function approximately on most iterations, without compromising the strong convergence properties of exact bundle methods. It was also shown that the recent method of Gaudioso et al. for finite min-max problems fits the partially inexact framework. In the work, its convergence results have been improved and useful modifications have been made. Numerical illustrations on stan­dard instances of the generalized assignment problem (GAP) are included.
    Bibliography p. 25-28
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/71/2007
    A Method of Centers with Approximate Subgradient Linearizations for Nonsmooth Convex Optimization
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. 22-23
    The paper presents a proximal bundle method for constrained convex optimization. It requires only evaluating the problem functions and their subgradients with an unkown accuracy ε. Employing a combination of the classic method of centers' improvement function with an exact penalty function, it does not need a feasible starting point. It asymptotically finds points with at least ε-optimal objective values that are ε-feasible. When applied to the solution of linear programming problems via column generation, it allows for ε-accurate solutions of column generation subproblems.
    23 stron ; 21 cm
    23 pages ; 21 cm
    Bibliography p. 22-23
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/39/2008
    An alternating linearization bundle method for convex optimization and nonlinear multicommodity flow problems
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    19 stron ; 21 cm
    19 pages ; 21 cm
    Bibliografia s. 17-19
    The paper gives a bundle method for minimizing the sum of two convex functions, one of them being known only via an oracle of arbitrary accuracy. Each iteration involves solving two subproblems in which the functions are alternately represented by their linearizations. The presented approach is motivated by applications to nonlinear multicommodity flow problems. Encouraging numerical experience on large scale problems is reported.
    Bibliography p. 17-19
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    A proximal bundle method with approximate subgradient linearizations
    Raport Badawczy = Research Report ; RB/67/2003
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    18 pages ; 21 cm
    The paper presents a proximal bundle method for minimizing a convex function f over a closed convex set. It only requires evaluating f and its subgradients with an accuracy ε>0, which is fixed but possibly unknown. It asymptotically finds points that are ε-optimal. When applied to Lagrangian relaxation, it allows for ε-accurate solutions of Lagrangian subproblems, and finds ε-optimal solutions of convex programs.
    Bibliography p. 17-18
    18 stron ; 21 cm
    Bibliografia s. 17-18
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/55/2006
    An Inexact Conic Bundle Variant Suited to Column Generation
    Autorzy:
    Kiwiel, Krzysztof
    Lemarechal, Claude
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    The paper presents a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a SIater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient vaIues with unknown accuracy. The proposed approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous - so that 0 is a natural Slater point - and an exact oracle may be time consuming. Finally, this convergence analysis empIoys arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems.
    Bibliography p. 42-45
    45 stron ; 21 cm
    Bibliografia s. 42-45
    45 pages ; 21 cm
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    An alternating linearization bundle method for convex optimization and nonlinear multicommodity flow
    Raport Badawczy = Research Report ; RB/37/2009
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    The paper presents a bundle method for minimizing the sum of two convex functions, one of them being known only via an oracle of arbitrary accuracy. Each iteration involves solving two subproblems in which the functions are alternately represented by their linearizations. The proposed approach is motivated by applications to nonlinear multicom­modity flow problems. Encouraging numerical experience on large scale problems is reported.
    Bibliografia s. 22-23
    23 stron ; 21 cm
    23 pages ; 21 cm
    Bibliography p. 22-23
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    An inexact bundle variant suited to column generation
    Raport Badawczy = Research Report ; RB/72/2007
    Autorzy:
    Kiwiel, Krzysztof
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. [29-30]
    [30] pages ; 21 cm
    Bibliography p. [29-30]
    [30] stron ; 21 cm
    The paper gives a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. The proposed approach is motivated by a number of applications in column generation, in which constarints are positively homogeneous - so that zero is a natural Slater point - and an exact oracle may be time consuming. Finally, this convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems.
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
      Wyświetlanie 1-9 z 9

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