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Available in the Mathcad tools do not allow to find the minimum of a function constructed from 10 Rosenbrock functions.

Available in the Mathcad tools do not allow to find the minimum of a function constructed from 10 Rosenbrock functions.

I'm looking for a ready-made algorithm "Direct search" (D.M. Himmelblau, Appled Nonlinear Programming, 1972) in Mathcad before 14. Is there such anyone? Thanks in advance.

J. Reyzenkind.

1 ACCEPTED SOLUTION

Accepted Solutions

Яков Рейзенкинд wrote:

f(x,y)= (100*(y1-x1^2)^2+(1-x1)^2)+(100*(y2-x2^2)^2+(1-x2)^2)+...+(100*(y10-x10^2)^2+(1-x10)^2)

This is a test function .

Perhaps the attached worksheet may be worth looking at; it uses the Hooke-Jeeves method.

Stuart

Modified version of worksheet posted in thread Hooke-Jeeves function TOMS178

View solution in original post

13 REPLIES 13

Some time ago there was a similar topic, here: Want to write MathCAD programm based on Maple 13 Code . Perhaps Walter has found a solution to this problem, try to ask him by using private message.

Vladimir, thanks for the tip!

No problem.

Just note that in addition to the implementation of this algorithm in Maple there is a whole toolbox in MATLAB (is called "Genetic Algorithm and Direct Search Toolbox"):

MATLAB Central - MathWorks - Genetic Algorithm and Direct Search Toolbox -

Genetic Algorithm and Direct Search Toolbox - Математика - Matlab.Exponenta.Ru

Vladimir! Thanks again.

Genetic algorithm on Mathcad Server:

Поиск глобального минимума по генетическому алгоритмупример 1пример 2пример 3

Dear Valery!

Thanks for sending the link. I ran the genetic algorithm on the Rosenbrock function (100*(y-x^2)^2+(1-x)^2). It works reliably. But in my test case x and y are vectors containing the 10 components. Unfortunately, I don't know how to enter vectors. In addition, I believe that for the problem with at least one minimum direct search will be more effective than genetic algorithm.

All the best.

Яков Рейзенкинд wrote: But in my test case x and y are vectors containing the 10 components.

???

Please show one example.

f(x,y)= (100*(y1-x1^2)^2+(1-x1)^2)+(100*(y2-x2^2)^2+(1-x2)^2)+...+(100*(y10-x10^2)^2+(1-x10)^2)

This is a test function .

Яков Рейзенкинд wrote:

f(x,y)= (100*(y1-x1^2)^2+(1-x1)^2)+(100*(y2-x2^2)^2+(1-x2)^2)+...+(100*(y10-x10^2)^2+(1-x10)^2)

This is a test function .

Perhaps the attached worksheet may be worth looking at; it uses the Hooke-Jeeves method.

Stuart

Modified version of worksheet posted in thread Hooke-Jeeves function TOMS178

Яков Рейзенкинд wrote:

f(x,y)= (100*(y1-x1^2)^2+(1-x1)^2)+(100*(y2-x2^2)^2+(1-x2)^2)+...+(100*(y10-x10^2)^2+(1-x10)^2)

This is a test function .

It is a function with 20 argument?

May be in this direction:

10Ros.png

Valery Ochkov wrote:

Яков Рейзенкинд wrote:

f(x,y)= (100*(y1-x1^2)^2+(1-x1)^2)+(100*(y2-x2^2)^2+(1-x2)^2)+...+(100*(y10-x10^2)^2+(1-x10)^2)

This is a test function .

It is a function with 20 argument?

May be in this direction:

...<image> ...

Interesting.  I get a different result using the Hooke-Jeeves algorithm;

The nested vector (3rd element of the result row vector) gives the co-ordinates whilst the last element of the result row vector gives the value of the Rosenbrock function at that location.  (the first two values are the Rosenbrock value at the starting values and the number of iterations, respectively)

Stuart

Stuart, Hello! Thank you very much for your materials. It will take time to understand them. All the best!

Jacob.

Thank You!

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