CODEWITHSUNDEEP
matlabvariables
Bob
Bob

Reputation: 3

Minimise a function of three variables over a range (MATLAB)

I want to minimise the maximum value the function f(a,b,c) takes over the range l <= c <= u for some lower and upper bounds l and u by changing the parameters a and b. I think I will need a double iteration but beyond that I have no idea how to begin.

I would greatly appreciate any of: an answer, help in phrasing this more clearly or information about where I can look to find the answer myself. I have tried to look elsewhere for an answer, but I am struggling to know what to search for.

EDIT: As an example, suppose f(a,b,c) is abs(g(a,c)-b). I have tried to vary a so that p(a) = max(g(a,c)) - min(g(a,c)) is minimised over c which would then easily allow me to compute what b should be, but the problem I am having is that g is not necessarily an easy to work with function.

Upvotes: 0

Views: 326

Answers (2)

Rody Oldenhuis
Rody Oldenhuis

Reputation: 38052

If you have the optimization toolbox, use fmincon:

X = fmincon(@(X) max(g(X(1),X(3))) - min(g(X(1),X(3))),... % the "cost function", i.e., what you want to minimize
            [0 0 1],...                                    % an initial guess for [a b c]
            [],[], [],[],...                               % (irrelevant for your problem)
            [-inf -inf 1], [+inf +inf u]);                 % lower and upper bounds for [a b c]

If you don't have the optimization toolbox, you can use my fminsearch wrapper minimize in exactly the same way. minimize uses fminsearch (which is included in standard MATLAB), but fminsearch cannot handle constraints, and minimize can.

What's more, that "initial estimate" can be hard to come by. You can do a simple grid search (as you suggested), but that tends to be tedious and slow, especially for larger problems. minimize can run without an initial estimate, in which case it will try an optimization a bunch of times for a bunch of random initial values within the bound constraints, and return the best one.

Upvotes: 0

Laure
Laure

Reputation: 373

You can use fminsearch and add a large negative value to out-of-bound solutions: 

% Your input
f = @(a,b,c) (a-2).^2+(b.^2-9)^2+sin(2*pi*c).^2;
u = 0.7;
l = -0.01;
% function to optimize
f2 = @(a) abs(f(a(1),a(2),a(3))+1e15*(a(3)>u|a(3)<l));
% Find a minima
fminsearch(f2,[1.6 1 0.2])

Upvotes: 1

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