Initial solution to a Convex Optimization problem

Question

I am aware that in a convex optimization problem, the initial solution does not matter as the algorithm guarantees convergence to the global minimum/maximum. But what if the initial solution does not satisfy one of the constraints? I.e. it is technically not a "solution" as it violates a constraint. Will using this as the initial guess still lead to the global solution?

Thanks.

Answer 1

It depends on what algorithm is being used, and even on the specific implementation of the algorithm: the violation of the constraint might create a situation which should never happen when the constraints are satisfied, and so the algorithm itself might not specify what to do in such a case.