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Convergence Rates for Hestenes' Gram-Schmidt Conjugate Direction Method without Derivatives in Numerical Optimization

Raihen, Nurul
http://orcid.org/0000-0003-2680-0658
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1494608232437057

Abstract Details

2017, Master of Science, University of Toledo, Mathematics.
In this paper we study convergence rates using quotient convergence factors and root convergence factors as described by Ortega and Rheinboldt for Hestenes' Gram- Schmidt conjugate direction method without derivatives. We do study this computa- tionally and analytically by comparing this conjugate direction method for minimizing a non quadratic function f with Newton's method for solving rf = 0. This method of Hestenes is di erent from that of Smith, Powell, and Zangwill in its mathematical development. All of these ideas have already been developed and based upon 1952 paper of Hestenes and Siefel, the 1980 book Conjugate Direction Methods in Opti- mization by Hestenes and the 1975 paper by Dennemeyer and Mookini. The primary purpose of this work is to provide details analytically and computationally of what has been done before.
Ivie Stein, Ph.D. (Advisor)
37 p.
Mathematics
Conjugate direction methods, Hestenes Gram-Schmidt conjugate direction method, numerical optimization

Recommended Citations

Citations

  • Raihen, N. (2017). Convergence Rates for Hestenes' Gram-Schmidt Conjugate Direction Method without Derivatives in Numerical Optimization [Master's thesis, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1494608232437057

    APA Style (7th edition)

  • Raihen, Nurul. Convergence Rates for Hestenes' Gram-Schmidt Conjugate Direction Method without Derivatives in Numerical Optimization. 2017. University of Toledo, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1494608232437057.

    MLA Style (8th edition)

  • Raihen, Nurul. "Convergence Rates for Hestenes' Gram-Schmidt Conjugate Direction Method without Derivatives in Numerical Optimization." Master's thesis, University of Toledo, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1494608232437057

    Chicago Manual of Style (17th edition)

toledo1494608232437057
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This open access ETD is published by University of Toledo and OhioLINK.