Question

How do you impose a constraint that all values in a vector you are trying to optimize for are greater than zero, using fmincon()?

According to the documentation, I need some parameters A and b, where A*x ≤ b, but I think if I make A a vector of -1’s and b 0, then I will have optimized for the sum of x>0, instead of each value of x greater than 0.

Just in case you need it, here is my code. I am trying to optimize over a vector (x) such that the (componentwise) product of x and a matrix (called multiplierMatrix) makes a matrix for which the sum of the columns is x.

function [sse] = myfun(x)        % this is a nested function
    bigMatrix = repmat(x,1,120) .* multiplierMatrix;
    answer = sum(bigMatrix,1)';
    sse = sum((expectedAnswer - answer).^2);
end

xGuess = ones(1:120,1);
[sse xVals] = fmincon(@myfun,xGuess,???);

Let me know if I need to explain my problem better. Thanks for your help in advance!

Answer 1

You can use the lower bound:

xGuess = ones(120,1);
lb = zeros(120,1);
[sse xVals] = fmincon(@myfun,xGuess, [],[],[],[], lb);

note that xVals and sse should probably be swapped (if their name means anything).

The lower bound lb means that elements in your decision variable x will never fall below the corresponding element in lb, which is what you are after here.

The empties ([]) indicate you’re not using linear constraints (e.g., A,b, Aeq,beq), only the lower bounds lb.

Some advice: fmincon is a pretty advanced function. You’d better memorize the documentation on it, and play with it for a few hours, using many different example problems.