Working examples for SemidefiniteOptimization

Question

It appears to me that for some types of invocation, SemidefiniteOptimization is not working for matrices larger that 2x2.

An example from help that works

a0 = {{0, 1}, {1, 0}};
a1 = {{1, 0}, {0, 0}};
a2 = {{0, 0}, {0, 1}};

SemidefiniteOptimization[2 x1 + 3 x2, 
 VectorGreaterEqual[{a0 + a1*x1 + a2*x2, 0}, {"SemidefiniteCone", 2}], {x1, x2}]
(* {x1 -> 1.22474, x2 -> 0.816497} *)

An alternative syntax is also available and working:

SemidefiniteOptimization[{2, 3}, {a0, a1, a2}]
(* {1.22474, 0.816497} *)

I now try to extend this to a trivially equivalent problem using 3x3 matrices. It returns unevaluated:

b0 = {{0, 1, 0}, {1, 0, 0}, {0, 0, 1}};
b1 = {{1, 0, 0}, {0, 0, 0}, {0, 0, 0}};
b2 = {{0, 0, 0}, {0, 1, 0}, {0, 0, 0}};
SemidefiniteOptimization[2 x1 + 3 x2, 
 VectorGreaterEqual[{b0 + b1*x1 + b2*x2, 0}, "SemidefiniteCone", 2}],
{x1, x2, x3}]

In the alternative syntax, the expected result is returned

SemidefiniteOptimization[{2, 3}, {b0, b1, b2}]
(* {1.22474, 0.816497} *)

Is this assessment correct, or am I missing something?

Answer 1

Fixing the syntax error in the second argument

SemidefiniteOptimization[2 x1 + 3 x2,  
  VectorGreaterEqual[{b0 + b1*x1 + b2*x2, 0}, {"SemidefiniteCone", 3}],
  {x1, x2}]

{x1 -> 1.22474, x2 -> 0.816497}

which matches the result from the alternative syntax:

SemidefiniteOptimization[{2, 3}, {b0, b1, b2}]

{1.22474, 0.816497}