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Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts

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Handbook on Semidefinite, Conic and Polynomial Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 166))

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Abstract

We review some of the recent enhancements of interior-point methods for the improved solution of semidefinite relaxations in combinatorial optimization and binary quadratic programming. Central topics include general interior-point cutting-plane schemes, handling of linear inequalities, and several warm-starting strategies. A practical implementation and computational results are also discussed.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Campus Box 170, 173364, 80217-3364, Denver, CO, USA

    Alexander Engau

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  1. Alexander Engau
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Correspondence to Alexander Engau .

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  1. Department of Mathematics and Industrial, Ecole Polytechnique Montreal, Édouard-Montpetit Boulevard 2350, Montreal, QC, Canada, H3C 3A7

    Miguel F. Anjos

  2. LAAS-CNRS, Avenue du Colonel Roche 7, 31077, Toulouse Cedex 4, France

    Jean B. Lasserre

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Engau, A. (2012). Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts. In: Anjos, M.F., Lasserre, J.B. (eds) Handbook on Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science, vol 166. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0769-0_17

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