How can I using fmincon on both vector variables and matrix variables

I have a optimization problem with two variables: x is a vector and U is a matrix. I want to solving it by fmincon. My question is, how I can write the fmincon. More exactly, how to write the objective function and constraints? Or I have to transform U into a vector variable.

Any suggestion is appreciated. Thanks!

[Torsten]

You have to use a vector X that comprises x and U, e.g.

U=U(:);

X = [x,U]

[Walter Roberson]

Is U effectively a constant input for the optimization? Or are the values in it being optimized too? Everything being optimized has to be packed into one variable.

[Jingyu Liu]

@Torsten That brings some difficulties when I write constraints. I should use X as the variable.

[Jingyu Liu]

@Walter Roberson U is a decision variable of the optimization and is not in the objective function.

[Walter Roberson]

When you write upper or lower bounds, or linear inequalities, or linear equalities, you do not need to refer to the variable that holds the "current" optimization parameters.

When you write nonlinear constraints, you most often use a function instead of an anonymous function. Inside the function you can take the inputs and unpack them into variables. For example,

function [c, ceq] = nonlcon(X)
    x = X(1:20);
    U = reshape(X(21:end), 5, 20);   %U is 5 x 20
    %now use x and U to compute c and ceq
end

I am not clear as to whether you are assigning values to U that are to be used consistently during the call to fmincon, or if fmincon is responsible for changing the U values as part of the optimization? fmincon does not handle integer constaints, so if they are decision variables to be optimized by fmincon then you have a problem.

If U is to be fixed for any one fmincon run, then you should be using a different approach entirely: http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Jingyu Liu]

@Walter Roberson Thanks for your suggestions. It really helps me a lot!

[Joshua Scott]

@Walter Roberson, What if you have both scalars and a matrix that need to be optimized?

Would I: Vectorize the matrix, reshape within the function getting called by fmincon, and reshape after fmincon?

Or am I missing a step?

Thank you for the guidance!

[Walter Roberson]

function [c, ceq] = nonlcon(X)  %example
    x = X(1);
    U = reshape(X(2:end), 5, 20);   %U is 5 x 20
    %now use x and U to compute c and ceq
end

And yes, after the optimization when you have the packed vector, you would to the same extraction to get the final values.

Answer 1

[Alan Weiss]

You might enjoy the problem-based approach, which does not require you to put all variables into one.

Alan Weiss

MATLAB mathematical toolbox documentation

[Jingyu Liu]

Thanks for your answer, it really helps me a lot!