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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?

Thanks.

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  • $\begingroup$ One technique is to 'minimize' the maximum constraint violation until the current solution becomes feasible. This is still a convex problem. $\endgroup$
    – copper.hat
    Dec 19, 2012 at 3:31

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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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  • $\begingroup$ Hi Robert, I see. Thanks for the input. I'm using a gradient based method by the way, in particular, Projected Gradient Descent. $\endgroup$
    – Tomas Jorovic
    Dec 19, 2012 at 1:50
  • $\begingroup$ I think in "projected gradient descent", starting from an infeasible point should not matter, because projections will bring it inside anyway. $\endgroup$
    – user25004
    Dec 19, 2012 at 4:19

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