Subproblem solvers#

This module implements the subproblem solvers of COBYQA.

The trust-region subproblems, i.e., the normal and tangential Byrd-Omojokun subproblems, are solved approximately using variations of the truncated conjugate gradient method. The function below implements these methods.

normal_byrd_omojokun(aub, bub, aeq, beq, xl, ...)

Minimize approximately a linear constraint violation subject to bound constraints in a trust region.

tangential_byrd_omojokun(grad, hess_prod, ...)

Minimize approximately a quadratic function subject to bound constraints in a trust region.

constrained_tangential_byrd_omojokun(grad, ...)

Minimize approximately a quadratic function subject to bound and linear constraints in a trust region.

The geometry-improving subproblems are solved approximately using techniques developed by Powell for his solver BOBYQA [DS1]. The functions below implement these techniques.

cauchy_geometry(const, grad, curv, xl, xu, ...)

Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region.

spider_geometry(const, grad, curv, xpt, xl, ...)

Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region.

References

[DS1]

M. J. D. Powell. The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report DAMTP 2009/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2009.