Warm start of the primal–dual method applied in the cutting-plane scheme

Warm start of the primal–dual method applied in the cutting-plane scheme

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Article ID: iaor20001102
Country: Netherlands
Volume: 83
Issue: 1
Start Page Number: 125
End Page Number: 143
Publication Date: Sep 1998
Journal: Mathematical Programming
Authors:
Keywords: duality
Abstract:

A practical warm-start procedure is described for the infeasible primal–dual interior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this field, the approach presented in this paper does not make the unrealistic assumption that the new cuts are shallow. Moreover, it treats systematically the case when a large number of cuts are added at one time. The technique proposed in this paper has been implemented in the context of HOPDM, the state of the art, yet public domain, interior-point code. Numerical results confirm a high degree of efficiency of this approach: regardless of the number of cuts added at one time (can be thousands in the largest examples) and regardless of the depth of the new cuts, reoptimizations are usually done with a few additional iterations.

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