Experimental Study Of The Broyden Class Updating Method For Solving Unconstrained Optimization Problems
ABSTRACT
Unconstrained optimization is an
optimization process where no restriction is placed on the range of the unknown
variable. Several methods can be adopted in the solution of unconstrained
optimization problems. In this work, emphasis is on the Broyden class updating
methods of Davidon-Fletcher-Powel (DFP)
algorithm, Broyden Fletcher Goldfarb Shannon(BFGS) algorithm and their linear
combinations. Linear constants ranging
from 0.1 to 0.9 are simulated in MATLAB and the numerical solutions are
extensively presented for
the following commonly tested functions: Freudenstein and Roth function, Beales
function and Woods function. The result of
the simulations in MATLAB environment and the graphical analysis in Microsoft
excel reveal that BFGS formula gives the best performance as it gives the same
convergence rate and better average time than DFP in all the test functions.
The average time and the number of iterations of the test functions increase as
the linear constant increases for the Linear Combination (LC) algorithm. It is
recommended that BFGS algorithm should be adopted when finding solution to
unconstrained optimization problems.
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MICHAEL, U (2022). Experimental Study Of The Broyden Class Updating Method For Solving Unconstrained Optimization Problems. Repository.mouau.edu.ng: Retrieved Apr 27, 2024, from https://repository.mouau.edu.ng/work/view/experimental-study-of-the-broyden-class-updating-method-for-solving-unconstrained-optimization-problems-7-2
UNIVERSITY, MICHAEL. "Experimental Study Of The Broyden Class Updating Method For Solving Unconstrained Optimization Problems" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 11 Oct. 2022, https://repository.mouau.edu.ng/work/view/experimental-study-of-the-broyden-class-updating-method-for-solving-unconstrained-optimization-problems-7-2. Accessed 27 Apr. 2024.
UNIVERSITY, MICHAEL. "Experimental Study Of The Broyden Class Updating Method For Solving Unconstrained Optimization Problems". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 11 Oct. 2022. Web. 27 Apr. 2024. < https://repository.mouau.edu.ng/work/view/experimental-study-of-the-broyden-class-updating-method-for-solving-unconstrained-optimization-problems-7-2 >.
UNIVERSITY, MICHAEL. "Experimental Study Of The Broyden Class Updating Method For Solving Unconstrained Optimization Problems" Repository.mouau.edu.ng (2022). Accessed 27 Apr. 2024. https://repository.mouau.edu.ng/work/view/experimental-study-of-the-broyden-class-updating-method-for-solving-unconstrained-optimization-problems-7-2