Yazar "Navidi, H." seçeneğine göre listele

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    Armijo rule and strong wolfe line search in generalized newton method
    (Maltepe Üniversitesi, 2009) Ketabchi, S.; Parandegan, M.; Navidi, H.
    The line search method is one of the two fundamental strategies to solve unconstrained optimization problem that have been developed up to now. The second strategy is trust region method. In the line search method, the success of the algorithm not only depends on well-chosen search direction but also well-chosen step length. In this paper we compare the Armijo step size regulation and Strong Wolfe conditions in generalized Newton algorithm to minimizing a piecewise quadratic convex function. This function arises from dual exterior penalty problem for the problem of finding normal solution of the system of linear equalities. Numerical experience for systems which are selected in NETLIB indicates the behavior of the two inexact line searches differs markedly.
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    Detecting and adjusting inconsistencies through a graphical and optimal approach in AHP
    (Maltepe Üniversitesi, 2009) Navidi, H.; Ahmadi, M.
    It is difficult to rank the alternatives in an ordinal or/and cardinal inconsistent AHP model. There is an iterative method to detect and adjust inconsistencies. In this study it is improved, lots of conditions omitted and it is confirmed by the numerical results by MATLAB. Gower Plot upon the singular value decomposition of paired comparisons matrix is used to detect inconsistencies. The improved optimization model provides suggested adjustments satisfying the bounds determinate by decision maker. After observing suggested numerical changes and Gower Plot the decision maker may revise iteratively the preferences to improve inconsistencies.
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    New algorithms based on the interior point method for convex quadratic programming
    (Maltepe Üniversitesi, 2009) Tahmasebzadeh, S.; Navidi, H.; Malek, A.
    This paper presents three new algorithms for solving convex quadratic programming problems subject to the linear constraints. These algorithms are based on the general theory of Karmarkar interior points techniques. The first one uses the Karmarkar idea and linearization of the objective function. The second and third algorithms are modification of the first algorithm using the Schrijver and Malek-Naseri approaches respectively. These three new schemes are tested against the algorithm of Kebbiche-Keraghel-Yassine (KKY). It is shown that these three new algorithms are more efficient and converge to the correct optimal solution, while the KKY algorithm does not converge in some cases. Numerical results are given to illustrate the performance of the new algorithms.
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    Solving linear programming using Newton method and Goldstein conditions
    (Maltepe Üniversitesi, 2009) Khosravi, P.; Navidi, H.; Malek, A.
    The aim of this paper is to find an exact least 2-norm solution to the dual linear programming problem and to generate an exact solution to the primal programming problem. The Newton method is proposed for solving linear programs with very large numbers of constraints and variables. We use Goldstein conditions in order to find a suitable step-size in each iteration. The proposed method is based on the apparently overlooked fact that the dual of an exterior penalty formulation of a linear program provides an exact least 2-norm solution to the dual of the linear program. Solving the dual yields an exact least 2-norm solution to the dual and the exact least 2-norm solution to dual problem can be used to generate an exact primal solution. A simple prototype of the method is given in eleven lines of MATLAB code. Encouraging computational results are presented.