solve a maximize problem by YALMIP

[reza mahjoub]

max D'AD

subject to: d'd<= E

 

D is m*n and A is m*m. 

E=constant

does it convex?and solvable by YALMIP?

[reza mahjoub]

the goal is finding optimum D.

[reza mahjoub]

the goal is finding optimum D. "d" is "D". I wrote it wrong.

[Johan Löfberg]

No it is not convex.

Yes it is "solvable" by YALMIP

However, it is trivially solved by computing eigenvalues (D will by definition be a scaled eigenvector associated with the largest eigenvalue of A). I assume you have a typo and D is a vector, as it makes no sense to maximize a matrix D'*A*D.

[reza mahjoub]

Thank you so much.

 

Yes. sorry D is a vector. If its not convex, then what type is that? 

[Johan Löfberg]

Depends on A. If A is positive semidefinite, you are maximizing a convex function, i.e., minimizing a concave function

Hence, if A is negative definite, you have a convex problem as you would be maximizing a concave function, i.e., minimizing a convex function.

[reza mahjoub]

Thanks a lot.