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Muna M. M. Ali
Mosul University

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New multi-step three-term conjugate gradient algorithms with inexact line searches Abbas Younis Al-Bayati; Muna M. M. Ali
Indonesian Journal of Electrical Engineering and Computer Science Vol 19, No 3: September 2020
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v19.i3.pp1564-1573

Abstract

This work suggests several multi-step three-term conjugate gradient (CG)-algorithms that satisfies their sufficient descent property and conjugacy conditions. First, we have  considered a number of well-known three-term CG-method, and we have, therefore, suggested two new classes of this type of algorithms which was based on hestenes and stiefel (HS) and polak-ribière (PR) formulas with four different versions. Both descent and conjugacy conditions for all the proposed algorithms are satisfied, at each iteration by using the strong Wolfe line search condition and it's accelerated version. These new suggested algorithms are some sort of modifications to the original  HS and PR  methods. These CG-algorithms are considered as a sort of the  memoryless BFGS update.  All of our new suggested methods are proved to be a  global convergent and numerically, more efficient than the similar methods in same area based on our selected set of used numerical problems.
Modified limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for unconstrained optimization problem Muna M. M. Ali
Indonesian Journal of Electrical Engineering and Computer Science Vol 24, No 2: November 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v24.i2.pp1027-1035

Abstract

The use of the self-scaling Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is very efficient for the resolution of large-scale optimization problems, in this paper, we present a new algorithm and modified the self-scaling BFGS algorithm. Also, based on noticeable non-monotone line search properties, we discovered and employed a new non-monotone idea. Thereafter first, an updated formula is exhorted to the convergent Hessian matrix and we have achieved the secant condition, second, we established the global convergence properties of the algorithm under some mild conditions and the objective function is not convexity hypothesis. A promising behavior is achieved and the numerical results are also reported of the new algorithm.
Co-Authors Abbas Younis Al-Bayati