I'm bit confused between Gradient descent and convex optimization using Lagrange Multipliers. I know that we use Lagrange multipliers when we have an optimization problem with one or more constraints.
From the answer of this question, it seems that we can also use gradient descent for constrained optimization.
So what is the difference between those two approaches? Mathematically I know how both of the approaches work but I don't understand when and why one is preferred over another? For example, for optimization of SVM (Support Vector Machine) problem, we use Lagrange multipliers instead of gradient descent.
I've found one similar question here. But the answer is not much clear. Any intuitive explanation/example will help. Thanks.