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Global error bounds for convex conic problems

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  • Zhang, S.

Abstract

In this paper Lipschitzian type error bounds are derived for general convex conic problems under various regularity conditions. Specifically, it is shown that if the recession directions satisfy Slater's condition then a global Lipschitzian type error bound holds. Alternatively, if the feasible region is bounded, then the ordinary Slater condition guarantees a global Lipschitzian type error bound. These can be considered as generalizations of previously known results for inequality systems. Moreover, some of the results are also generalized to the intersection of multiple cones. Under Slater's condition alone, a global Lipschitzian type error bound may not hold. However, it is shown that such an error bound holds for a specific region. For linear systems we show that the constant involved in Hoffman's error bound can be estimated by the so-called condition number for linear programming.

Suggested Citation

  • Zhang, S., 1998. "Global error bounds for convex conic problems," Econometric Institute Research Papers EI 9830, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1544
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    References listed on IDEAS

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    1. J.F. Sturm & S. Zhang, 1998. "On Sensitivity of Central Solutions in Semidefinite Programming," Tinbergen Institute Discussion Papers 98-040/4, Tinbergen Institute.
    2. A.G. Holder & J.F. Sturm & S. Zhang, 1998. "Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming," Tinbergen Institute Discussion Papers 98-003/4, Tinbergen Institute.
    3. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1997. "Duality Results for Conic Convex Programming," Econometric Institute Research Papers EI 9719/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Michael J. Todd, 1990. "A Dantzig-Wolfe-Like Variant of Karmarkar's Interior-Point Linear Programming Algorithm," Operations Research, INFORMS, vol. 38(6), pages 1006-1018, December.
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