I am a network engineer engaged in optimizing network functionalities and have observed a certain progression in the development of optimization solvers. Notably, it seems common for developers to first create solvers for second order cone optimization (or semidefinite optimization) and subsequently for exponential cone optimization. For instance, this development path is evident with solvers like MOSEK. Moreover, it appears challenging to find robust solvers for exponential cone optimization beyond MOSEK.
Therefore, out of pure curiosity my question is "Does exponential cone optimization is more challenging to solve than second order cone optimization ?"
This inquiry stems from the observation that the exponential cone is a type of nonsymmetric cone, which I suspect might complicate the solving process for standard solvers like SDPT-3. Particularly, I think that numerical method for symmetric cone cannot be reused on non-symmetric cone. However, my understanding is also conflicted by the notion that the difficulty level might be comparable since both problem types are convex.
Could anyone with experience or insights in this area kindly clarify this matter for me? Any explanations or resources shared would be greatly appreciated.
Thank you for your enthusiasm !