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On a Commutative Class of Search Directions for Linear Programming over Symmetric Cones

Author

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  • M. Muramatsu

    (The University of Electro-Communications)

Abstract

The commutative class of search directions for semidefinite programming was first proposed by Monteiro and Zhang (Ref. 1). In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Complexity results are established for short-step, semilong-step, and long-step algorithms. Then, we propose a subclass of the commutative class for which we can prove polynomial complexities of the interior-point method using semilong steps and long steps. This subclass still contains the Nesterov–Todd direction and the Helmberg–Rendl–Vanderbei–Wolkowicz/Kojima–Shindoh–Hara/Monteiro direction. An explicit formula to calculate any member of the class is also given.

Suggested Citation

  • M. Muramatsu, 2002. "On a Commutative Class of Search Directions for Linear Programming over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 595-625, March.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:3:d:10.1023_a:1017920200889
    DOI: 10.1023/A:1017920200889
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    Cited by:

    1. Huali Zhao & Hongwei Liu, 2018. "A New Infeasible Mehrotra-Type Predictor–Corrector Algorithm for Nonlinear Complementarity Problems Over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 410-427, February.

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