Role of initial starting point in convergence of pattern search with non-linear constraints
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When non-linear constraints are in in question, MATLAB has a variation of pattern search that used the augmenetd Lagrangian barrier algorithm to ensure solutions are feasible. A drawback of this approach , as far as I can se is that infeasible initial points (those that violate the non-linear constraints) would hamper the internal iterations as tehy would lead to the objective function being evaluated to infinity (because of the lagrangian barriers). How (If at all) does pattern search account for these anomalies?
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Alan Weiss
on 16 Jul 2014
The nonlinear constraint algorithm is described here. I believe that the nonnegative shifts s_i keep the penalty function finite even if c(x0) is positive. And there is no term that makes an infinity for ceq(x0).
Alan Weiss
MATLAB mathematical toolbox documentation
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Alan Weiss
on 17 Jul 2014
I believe that all general nonlinear solvers depend on an initial point, and can fail to find a feasible solution for some initial points. This is certainly true for MATLAB, but I think it is generally true. The caveat is for some structured nonlinear problems such as quadratic, you don't need an initial point.
Alan Weiss
MATLAB mathematical toolbox documentation
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