Minimize norm(x,inf) (Moderator note: nonconvexity is due to something else in model)

Nonconvex
1

I have faced a problem in my research area. I want to minimize the maximum absolute value of F*x , in which x’s power must be at leas unit. It means that the constraint is norm(x,2)==1
How could I define a problem so I can CVX to solve it

cvx_begin
variable x(n)
minimize norm(F*x,inf)
subject to
norm(x,2)==1
cvx_end

2

Your problem is obviously nonconvex. The relaxation

norm(x,2)<=1

leads to a convex problem but then x=0 is the optimal solution.
And if your problem is nonconvex Cvx cannot solve your problem.

4

Thanks for your help.
That was the first solution that came to my mind ,but as you sait it did not work.
Can it be solved via fmincon function in Matlab?

5

Yes, FMINCON can try to find a local optimum.