International Journal of Computer Mathematics Vol.
81, No.9, September 2004, pp. 1145-1152
Q Taylor & Francis
~
Tay1or&FrancisGroup
OPTIMIZATION IN Rn BY COGGIN'S METHOD
O. M. BAMIGBOLA'* and F. B. AGUSTOb
a Department of Mathematics, University of /lorin, /lorin, Nigeria;
b Department of Pure and Applied Mathematics, Ladoke Akintola University of
Technology, Ogbomoso, Nigeria
(Revised 10 December 2002; lnfinalform 2 April 2004)
A higher dimensional Coggin's algorithm for the resolution of optimization problems is developed for the n-dimensional Euclidean
space JR" by using a prescribed search parameter. The method is shown to be accurate and rapidly converging.
Keywords: Coggin's method; Multivariable functions; Interpolation; Directional search
C.R. Category: G.1.7
1 INTRODUCTION
Let us consider the unconstrained problem
Minimize f (x)
x
(x E ]Rn),
(1)
where f(x) is the objective function and x* is the minimizer. The optimum is obtained along
the line X(A) = x* + A *s with A* denoting the search parameter and s denoting the search direction.
The aim of all one-dimensional minimization techniques is to find A *, the smallest nonnegative value of A, for which the function
f(A) = f(x + AS)
(2)
attains a local minimum.
Hence if the original function f (x) is expressible as an explicit function of Xi (i = 1,2, . . .
,n), we can readily write expression (2), for any specific vector s and then solve (df(A)/dA) =
0 to obtain A* in terms of x and s. However, in many practical problems, the function f(A)
cannot be expressed explicitly in terms of A. In such cases, the interpolation method can be used
to find the value of A * .
* Corresponding author. E-mail: ombamigbola@hotmail.com
ISSN 0020-7160 print; ISSN 1029-0265 online @ 2004 Taylor & Francis Ltd
DOl: 10.1080/03057920412331272162