# Successive Approximation Method & MOSEK

First of all, I would like to thank everyone who have contributed to CVX solver. It makes my life a little easier than dealing with a solver directly; such as, MOSEK.

I have been working with MOSEK before, but I am a little confuse about the successive approach method. I’m trying to solve a logistic regression problem with some additional constraints. For simplicity, let’s consider the Logistic Regression example provided by CVX, which can be found here:

Logistic Regression Example by CVX

What does CVX exactly do with exponentials ? I would like to understand why it adds 8 more variable for each exponential variable and 5 additional constraints for each exponential constraint?

Thanks

None of the solvers that CVX relies upon can handle the exponential cone, or functions that are built using it, like the logistic function. Therefore, CVX is having to approximate each exponential with a polynomial. And since no polynomial can represent the entire range of an exponential precisely, CVX must repeatedly adjust the region of approximation until the polynomial approximation is a good fit at the solution.

MOSEK does have a different solver for smooth convex functions that can handle the logistic function natively, but CVX cannot connect to that solver.

I looked over the Mosek manual but I couldn’t find how to write the exponential or logarithmic functions using Mosek. Any idea on that?

Also, Can MOSEK (or CVX) estimate a an integer solution for exponential problems ( for ex. using mixed-integer programming)?

Thanks mcg for your answer. I looked over the Mosek manual but I couldn’t find how to write the exponential or logarithmic functions using Mosek. Any idea on that?

Also, Can MOSEK (or CVX) estimate a an integer solution for exponential problems ( for ex. using mixed-integer programming)?

Sorry, I have no experience with MOSEK’s smooth convex solver. And no, CVX does not handle integer constraints with exponential constraints, and nor does MOSEK, I suspect.

the problem doesn’t have exponential constraint (sorry if I misinterpreted it). It has a cost function that involves an exponential and one of the variables is an integer.