Quadratic nonconvex inequality constraint


(ciel bleu) #1

hello, i have a convex optimization problem and i want to add a new nonconvex inequality as below:

norm(AA’-A’A)<= er
A:matrix variable & er:known scalar

how can i add this so i can use cvx to solve my optimization?
any help is greatly appreciated :slight_smile:


Orthogonal matrix variable
(Mark L. Stone) #2

This is non-convex, so it can not be used in CVX.


(ciel bleu) #3

I couldn’t prove its convexity so i used numerical examples. could you please tell me a good way to check convexity of complex functions?


(Mark L. Stone) #4

Examine the definiteness of the Hessian, if it exists. or better yet, if you can, try proving it by applying the DCP rules, in which case if you succeed, you will know how you can enter it into CVX. if you can formulate the Hessian, it is often easy to show the function is not convex (or concave) by numerically evaluating its eigenvalues at various argument values. If the Hessian has both positive and negative eigenvalues, the function is neither convex nor concave, and not possible be used in CVX.

Perhaps you can read at least the first four chapters of “Convex Optimization” by Boyd and Vandenberghe http://web.stanford.edu/~boyd/cvxbook/