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Accelerated Double Direction Method for Solving Unconstrained Optimization Problems

Author

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  • Milena J. Petrović
  • Predrag S. Stanimirović

Abstract

An iterative method for solving a minimization problem of unconstrained optimization is presented. This multistep curve search method uses the specific form of iteration with two direction parameters, the approximation of Hessian by appropriately constructed diagonal matrix, and the inexact line search procedure. It is proved that constructed numerical process is well defined under some assumptions. Considering certain conditions, the method is linearly convergent for uniformly convex and strictly convex quadratic functions. Numerical results arising from defined algorithms are also presented and analyzed.

Suggested Citation

  • Milena J. Petrović & Predrag S. Stanimirović, 2014. "Accelerated Double Direction Method for Solving Unconstrained Optimization Problems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jnlmpe:965104
    DOI: 10.1155/2014/965104
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    Cited by:

    1. Milena J. Petrović & Ana Vučetić & Tanja Jovanović Spasojević, 2024. "Hybrid Modified Accelerated Gradient Method for Optimization Processes," Mathematics, MDPI, vol. 12(5), pages 1-13, February.
    2. Milena J. Petrović & Dragana Valjarević & Dejan Ilić & Aleksandar Valjarević & Julija Mladenović, 2022. "An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    3. Vladimir Rakočević & Milena J. Petrović, 2022. "Comparative Analysis of Accelerated Models for Solving Unconstrained Optimization Problems with Application of Khan’s Hybrid Rule," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    4. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.

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