Function “atan” supported in CVX？

Nonconvex
#1

Hi all,

There is a inverse tangent function in my constraint. Actually, I use the Matlab built-in function “atan”. The expression of this constraint is:
x - atan(y) <= 0,
where x and y are scalar variable, and y>=0.

However, an error appears: Undefined function ‘atan’ for input arguments of type ‘cvx’.
Does this mean function “atan” is not supported in CVX？

Thx!
Yvan

#2

`atan is neither convex nor concave, so not supported by CVX.

#3

Thank you Mark. In my case, y>=0, so -atan(y) is convex in this domain of definition. And the constraint x-atan(y) is a convex set.

Is there anything I can do to make this constraint accepted by CVX? (Maybe something like the CVX build-in function “square_pos”?)

#4

See my answer at How to introduce the arctan function into cvx

#5

Thank you! This is helpful. I decide to try successive approximation.

By the way, in the future, will CVX include features to deal with function like arctan and tan? Maybe:

  1. add built-in function, e.g., “atan_pos”?
  2. include built-in successive approximation for arctan like what have been done for log function?
#6

I doubt any of that will ever be added to CVX, which is not in a very active state of development (I am not the developer).

#7

OK, I see. Thanks for reply!

#8

Hello, I also encountered the same problem, but I don’t know how to make continuous approximation of this atan function. How do you solve it? Looking forward to your reply

#9

The way you “solve it” is to to use some tool other than CVX. For instance, YALMIP, which allows non-convexities and has support for atan (and also supports atan2 in its develop branch https://groups.google.com/g/yalmip/c/diLhQLh5bN8 )

#10

Thank you! This is helpful. I will try it.