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Title

A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems

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Abstract

 In this paper, we solve Unconstrained optimization problem using a free Line search Steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value of this matrix is not greater than the number of variables of the problem. Then, using this double parameter scaled quasi Newton formula, an explicit formula for calculating the step length in the Steepest descent method is presented and therefore, this method does not require the use of approximate methods for calculating step length. The numerical results obtained from the implementation of the algorithm in MATLAB software environment are presented for some optimization problems. These results show the efficiency of the proposed method in comparison with other existing methods.

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    APA: Copy

    Bidabadi, Narges. (2021). A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(26 ), 0-0. SID. https://sid.ir/paper/969369/en

    Vancouver: Copy

    Bidabadi Narges. A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;6(26 ):0-0. Available from: https://sid.ir/paper/969369/en

    IEEE: Copy

    Narges Bidabadi, “A Free Line Search Steepest Descent Method for Solving Unconstrained Optimization Problems,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 26 , pp. 0–0, 2021, [Online]. Available: https://sid.ir/paper/969369/en

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    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
    مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources
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