Hacky unconstrained vs. constrained numerical optimization

2 views (last 30 days)
Evan on 1 May 2017
Short version: Why is unconstrained optimization with a constraint "hacked" into the objective function working while constrained optimization isn't?
Long version:
I'm trying to find a p x n subspace U which explains an arbitrary amount of variance in my m x p dataset X. The objective function is:
projection = U'*X';
fracVar = sum(var(projection'))/totalVar;
fVal = (targetVar - fracVar)^2;
I tried using `fmincon()` with a nonlinear equality constraint that U must have orthogonal columns of unit norm:
temp = norm(U'*U - eye(size(U,2)));
I can not get this to work. It fails in different ways, including not getting anywhere near the desired fraction of variance and failing to meet the constraints.
However, if I use `fminsearch()` instead and change the objective to:
projection = orth(U)'*X';
fracVar = sum(var(projection'))/totalVar;
fVal = abs(targetVar - fracVar);
and then use `orth()` again on the result, it seems to work perfectly. I thought this would be the "wrong" way as I'm basically hacking the constraint into the objective.
What is an explanation for this? Is there a "correct" approach to this problem?

Categories

Find more on Nonlinear Optimization in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!