Help with Minimization
of Functions of Several Variables
Prof. Richard B. Goldstein
Rosenbrock's Test Function
calculus formula |
100(y - x2)
2 + (x - 1)2 |
JavaScript Function |
100*Math.pow(1*x[2]-x[1]*x[1],2)+1*Math.pow(x[1]-1,2) |
Initial point |
(-1.2, 1) |
minimum point |
(1, 1) |
The program was tested and worked well with a number of test functions
like
the Rosenbrock and Powell test functions. The program required
calculation
of the gradient, a linear search with unknown starting interval, and the
BFGS (Broyden - Fletcher - Goldfarb - Shanno) formula for a quasi-Newton
method. The above level curves show the difficulty of approaching the
minimum point at (1, 1). The level curves appear as narrow twisted
ellipses
close to the parabola y = x2
Return to the Minimization of n Variables
procedure