I have a relaxed convex problem (Conic) that can be expressed using two formulations. When solved using CPLEX, I obtained the same global solution. However, one formulation yielded the global solution in much faster time than the other. My question is how to explain these finding scientifically?
My guess is that the faster algorithm has a smaller feasible space which allow the solver to find the solution in a faster way but I can't prove this or even know if this is really the case. Any suggestion that can help in comparing the performance?