Norm of non-separable bilinear term


#1

Hello,
I would like to know if CVX can handle a constraint of the form
||x * y|| <= a
where x and y are bounded continuous variables and a is a constant.

Thanks.


(Mark L. Stone) #2

#3

Let me rephrase my question.
Any norm is convex.
Why is the expression
|x * y|| <= a
where x and y are bounded continuous variables and a is a constant.
considered non-convex?


(Mark L. Stone) #4

Any norm is a convex function of an affine argument, which a bilinear term is not.


(Michael C. Grant) #5

Prat, a basic understanding of convex analysis and optimization is required in order to properly use CVX. Please consider, for instance, any course built around the book Convex Optimization by Boyd & Vandenberghe. The initial 3 chapters of that book will help you understand concepts like this.