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.
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Minimize approximately a linear constraint violation subject to bound constraints in a trust region. |
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Minimize approximately a quadratic function subject to bound constraints in a trust region. |
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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.
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Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. |
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Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. |
References
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.