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

A practical warm-start procedure is described for the infeasible primal-dualinterior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this eld, 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 con rm a high degree of e ciency 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. Key words. Warm start, primal-dual algorithm, cutting-plane methods.  Supported by the Fonds National de la Recherche Scienti que Suisse, ...

• Type: Journal
• Year: 1998
• Where: MP
• Authors: Jacek Gondzio
• Keywords: Cutting-plane Methods, Infeasible Primal-dualinterior-point Method, MP 1998, Practical Warm-start Procedure