Thanks for the sample code; I can reproduce your problem and have a fix.
On each step, the MMA algorithm calls NLopt recursively to optimize a
convex local model of the objective and constraints in a trust
region. (Technically, it solves the dual problem rather than the
primal one.) It looks like you are running into a limitation stemming
from NLopt not solving this subsidiary problem accurately enough.
You can override NLopt's defaults for solving this subsidiary problem
by the set_local_optimizer method. In particular, add the following
lines to your computeNLOpt function before calling optimize:
nlopt::opt dual_opt(nlopt::LD_LBFGS,n);
dual_opt.set_ftol_rel(1e-14);
optim.set_local_optimizer(dual_opt);
This fixes the problem for me.
In the next release, I should probably lower the default tolerance for
the dual problem. You can alternatively do this yourself by applying
the following patch to api/optimize.c. Change:
nlopt_set_ftol_rel(dual_opt, LO(ftol_rel, 1e-12));
to
nlopt_set_ftol_rel(dual_opt, LO(ftol_rel, 1e-14));
Steven
PS. You can feel free to set a tolerance of zero for inequality
constraints. A nonzero tolerance is only really important for
equality constraints.
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