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.