Cvx error when multiply with -1j

1

Hi,
I have a scalar that is convex and real, lets say “x”.
when trying to multiply it with -1jx I get the following error:
Disciplined convex programming error:
Cannot perform the operation: {complex affine} . {convex}

Now although some may argue that -1j is in fact a affine function, I should note that multiplying x by real scalar is fine.
Am I missing something?

2

http://cvxr.com/cvx/doc/dcp.html#expression-rules

  • A valid convex expression is
  • a valid constant or affine expression;
  • a valid call to a function in the atom library with a convex result;
  • an affine scalar raised to a constant power p≥1
    , p≠3,5,7,9,…* * ;
  • a convex scalar quadratic form—see Scalar quadratic forms ;
  • the sum of two or more convex expressions;
  • the difference between a convex expression and a concave expression;
  • the product of a convex expression and a nonnegative constant;
  • the product of a concave expression and a nonpositive constant;
  • the negation of a concave expression.
  • A valid concave expression is
  • a valid constant or affine expression;
  • a valid call to a function in the atom library with a concave result;
  • a concave scalar raised to a power p∈(0,1)
  • ;
  • a concave scalar quadratic form—see Scalar quadratic forms ;
  • the sum of two or more concave expressions;
  • the difference between a concave expression and a convex expression;
  • the product of a concave expression and a nonnegative constant;
  • the product of a convex expression and a nonpositive constant;
  • the negation of a convex expression.

You will not see in these lists a provision for multiplying a convex expression by an imaginary or complex number. Hence your error message.

Let x be a CVX variable. Consider the convex expression x^2. Then consider the expression 2*x^2; that is also convex. What is the convexity of 1j*x^2 or -1j*x^2 ; they are neither convex nor concave, so CVX will not allow them.

3

Thanks for the explantion!
I do wonder though, is it possible in cvx framework to fft a convex variable? Say if the sparse condition is in the dual transform.