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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?


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One technique is to 'minimize' the maximum constraint violation until the current solution becomes feasible. This is still a convex problem. – copper.hat Dec 19 '12 at 3:31

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.

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Hi Robert, I see. Thanks for the input. I'm using a gradient based method by the way, in particular, Projected Gradient Descent. – Tomas Jorovic Dec 19 '12 at 1:50
I think in "projected gradient descent", starting from an infeasible point should not matter, because projections will bring it inside anyway. – user25004 Dec 19 '12 at 4:19

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