I have a 0-1 second order cone (SOC) problem and I need to know the complexity of solving this problem if branch and cut (B&C) method is used?. The way I addressed this question is as following:
The 0-1 SOC problem can be solved using B&C method which has an exponential worst case complexity, i.e., O(2^n). At each node of B&C method, the relaxed problem is a SOC problem which can be solved using an interior point method which has a polynomial-time complexity. However, I do not have an expression for the complexity of the interior point method yet. Assuming this complexity is O(n). Then, I can claim that the complexity of solving the 0-1 problem using B&C method is O(2^n) times O(n).
