Dear Forum Members,
I am working on robust linear optimization. I use ellipsoid uncertainty. Vector x is the variable. Therefore original linear constraint a_{0}^{T}x<=b becomes a conic quadratic inequality in robust version:
[a_{0}^{T}x+ \omega \sqrt{\sum_{l=1}^{L} ([a^{l}]^{T}x)^{2}} \leq b_{0}.
According to Robust Optimization book by Ben tal et. al, this is convex. My problem is I am having problem with implementing this in Matlab.
When I tried I received
Disciplined convex programming error:
** Illegal operation: sqrt( {convex} ).**
This is my code.
omega*sqrt(trace(A*X')) +trace(R*X') <=alpha;
here X is a 2n by 2n variable matrix and A and R are 2n by 2n parameter matrices. trace(R*X’) is equivalent to Frobenius inner product of R and X i.e. sum_{i} sum_{j} R_{ij}X_{ij}. Omega and alpha are constant numbers like 0.01.
I don’t see how that line of code would generate that error message. It should generate an error message, but not that one. That code is on a path to failure for various reasons.
For the first term, you want something along the lines of omega*norm([A(:,1)'*x,A(:,2)'*x,...,A(:,L)'*x])
where I leave it you to fix up the indexing and subscripting of A, x (X) or whatever, and other details, matricize it, etc… if you make the argument of norm into a matrix, then you can use 'fro'. Note that I am starting from the constraint in your text, and make no use of your code, which looks flat out wrong (if it’s not, please tell us why it’s not).
Thank you Mark. I will start the implementation with your suggestions and fix the rest.
Best.
Maybe you can use norm(A'*x) for suitably defined A which horizontally stacks the column vectors a_l, and where x is a column vector.
