title: Forcing fmincon to consider candidate solutions only from a specific set
body: <p>Is it possible to force MATLAB's fmincon to generate candidate points from a specific set of points that I supply? I ask this because if this were possible, it would greatly reduce computation complexity, and knock out a couple of constraints from the optimization.</p>
  
  <p><em>Edited to add more info:</em> Essentially, I'm looking for a set of points in a high dimension space which satisfy a particular function (belonging to that space), along with a couple of other constraints. The objective function minimizes the total length of the path formed by these points. Think generalized geodesic problem, attempted via non-linear optimization. While I manage to get near a solution while using fmincon, it is painfully slow and is prone to get stuck in local minima. I already have a sizeable set of data-points which satisfy this high-dimensional function, and have no compulsion that this new set of points not belong to this pre-existing set.</p>