MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 111)

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• Call a function with the name:

t that implements the

gradient descent algorithm for minimizing the aforementioned

function. The calling syntax of this function should be:

“[MinPoints, xVals] =

t(fun, x, lr, maxIterNum, tol)”

fun is the function name “@funToMin”, x is a row vector with the

user’s guess (starting value) about the minimum of the function. The

input argument “lr” is the learning parameter a that should be set to

0.1 if not specified by the user. “maxIterNum” is as before the

maximum number of iterations that should be set to 100 if not

specified and “tol” is the tolerance concerning the norm of the

updating component of the point x (stopping criterion) and should be

set to 1e-6 is not specified. The function returns “MinPoints” that if

the algorithm has converged is the point where the function is

minimized, and “xVals” that is an m-by-2 array with the set of the

values of x at each iteration of the algorithm (m is either equal to:

maxIterNum” or a smaller number if the algorithm converges).

This function should call another function with the name:

and with the following calling syntax:

“GradsVals =

s(fun,x)”

that takes as input a function and a single coordinate point and

returns the gradient vector at that point. Use the two sided finite

difference method explained before. For the above, use as initial

point: x

=[0 0].

After you have called the function, plot on the contour figure the

algorithm’s trajectory to the minimum found in “xVals”. Call once

more the function with x

=[-1 -2] and add the new trajectory to the

contour figure. Use “lr”=0.25 and “maxIterNum”=200. Use

enter a text that indicates the trajectory.

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur Page 111