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Fast approximations for common geodesic measurements

COBYLA2 is an implementation of Powell's nonlinear derivative free constrained optimization that uses a linear approximation approach. The algorithm is a sequential trust region algorithm that employs linear approximations to the objective and constraint functions, where the approximations are formed by linear interpolation at n + 1 points in the space of the variables and tries to maintain a regular shaped simplex over iterations. It solves nonsmooth NLP with a moderate number of variables (about 100). Inequality constraints only. The initial point X is taken as one vertex of the initial simplex with zero being another, so, X should not be entered as the zero vector.