In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the loqo algorithm and provide extensive numerical results on the CUTEr test set and on warmstarting in the context of quadratic, nonlinear, mixed integer nonlinear, and goal programming.
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Research of the first author is sponsored by ONR grant N00014-04-1-0145. Research of the second author is supported by NSF grant DMS-0107450.
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Benson, H.Y., Shanno, D.F. Interior-point methods for nonconvex nonlinear programming: regularization and warmstarts. Comput Optim Appl 40, 143–189 (2008). https://doi.org/10.1007/s10589-007-9089-x
- Interior-point methods
- Nonlinear programming
- Penalty methods