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Cone-LP's and semidefinite programs: Geometry and a simplex-type method

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Integer Programming and Combinatorial Optimization (IPCO 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1084))

Abstract

We consider optimization problems expressed as a linear program with a cone constraint. Cone-LP's subsume ordinary linear programs, and semidefinite programs. We study the notions of basic solutions, nondegeneracy, and feasible directions, and propose a generalization of the simplex method for a large class including LP's and SDP's. One key feature of our approach is considering feasible directions as a sum of two directions. In LP, these correspond to variables leaving and entering the basis, respectively. The resulting algorithm for SDP inherits several important properties of the LP-simplex method, in particular, the linesearch can be done in the current face of the cone, similarly to LP, where the linesearch must determine only the variable leaving the basis.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Gábor Pataki

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  1. Gábor Pataki
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William H. Cunningham S. Thomas McCormick Maurice Queyranne

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© 1996 Springer-Verlag Berlin Heidelberg

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Pataki, G. (1996). Cone-LP's and semidefinite programs: Geometry and a simplex-type method. In: Cunningham, W.H., McCormick, S.T., Queyranne, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 1996. Lecture Notes in Computer Science, vol 1084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61310-2_13

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  • DOI: https://doi.org/10.1007/3-540-61310-2_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61310-7

  • Online ISBN: 978-3-540-68453-4

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