One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal–dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set of linear and mixed integer programming problems.
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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. An exact primal–dual penalty method approach to warmstarting interior-point methods for linear programming. Comput Optim Appl 38, 371–399 (2007). https://doi.org/10.1007/s10589-007-9048-6
- Interior-point methods
- Linear programming
- Penalty methods