Help with Minimization
of Functions of Several Variables

Prof. Richard B. Goldstein

More detailed
help with

JavaScript Syntax

Rosenbrock's Test Function

Rosenbrock's 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

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