Can Matlab be used to perform the optimization of a second order model to determine the optimum points?

I have a second order model with 4 variables and I plotted the surface plot of the response against 2 of the variables while keeping the other 2 fixed at their mid level. Is there a code to locate the stationary or turning point of the plot

[John Petersen]

Not real clear on your question. What do you mean by stationary or turning point of the plot?

[Chimezie Umezie]

Thank you for your comment.I mean to say the value(or coordinates) of the factors x1,x2,x3 and x4 that give the maximum(or minimum response). I used LinearModel.fit to fit the data to a full quadratic model.If you don't mind sending your email address I can send the M-file. I am a student of University of Aberdeen and I am writing my dissertation. I need help on this.

Thank you

Answer 1

[Alan Weiss]

You can find a minimum of a function using fminsearch. If you have optimization Toolbox, use fminunc.

You can find a maximum by negating the function and then searching for a minimum (see Maximizing Functions).

To find a saddle point, you will need to do more work, and will need Optimization Toolbox. Find the gradient of the function (if you have Symbolic Math Toolbox, you can do this easily, as shown in this example). Then find the root of the gradient using fsolve.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation