# nonsymmetric cone and Euclidean Jordan Algebra

I have a mathematical constraint which is a summation of exponential functions: $$f = e^{x + y}$$. Function $$f$$ is obviously convex. However, when I include this constraint in my model, MOSEK complains that the constraints with equations $$f$$ is a non symmetric cone. Upon doing a bit of research, I found notes about Euclidean Jordan Algebra being a unifying algebra for symmetric cones. I have 2 questions, (1) How do I prove that indeed the constraint with functions $$f$$ belongs in a non symmetric cone? (2) I do not understand how convexity relates to symmetric cones only as required by Euclidian Jordan Algebra. Please help?

• How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones. – Michal Adamaszek Mar 12 at 9:07
• Hi Michael,This is the actual constraint: $\sum\limits_{i}\sum\limits_{j}e^{ln2(x_{i} + x_{j})} \leq 0$ – P. Khoza Mar 12 at 9:31
• That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with. – Michal Adamaszek Mar 12 at 9:36
• I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + \ (cp.exp(math.log(2) * (x[0] + x[1])) + \ (cp.exp(math.log(2) * (x[0] + x[2])) + \ (cp.exp(math.log(2) * (x[0] + x[3])) + \ (cp.exp(math.log(2) * (x[1] + x[0])) + \ (cp.exp(math.log(2) * (x[1] + x[1])) + \ \vdots\ (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone. – P. Khoza Mar 12 at 9:49
• You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver. – Michal Adamaszek Mar 12 at 9:53