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Error Bounds of Constrained Quadratic Functions and Piecewise Affine Inequality Systems

Author

Listed:
  • K.F. Ng

    (Chinese University of Hong Kong)

  • X.Y. Zheng

    (Chinese University of Hong Kong)

Abstract

We consider the error bounds for a piecewise affine inequality system and present a necessary and sufficient condition for this system to have an error bound, which generalizes the Hoffman result. Moreover, we study the error bounds of the system determined by a quadratic function and an abstract constraint.

Suggested Citation

  • K.F. Ng & X.Y. Zheng, 2003. "Error Bounds of Constrained Quadratic Functions and Piecewise Affine Inequality Systems," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 601-618, September.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:3:d:10.1023_b:jota.0000004873.30548.ca
    DOI: 10.1023/B:JOTA.0000004873.30548.ca
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    References listed on IDEAS

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    1. Wu Li & Ivan Singer, 1998. "Global Error Bounds for Convex Multifunctions and Applications," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 443-462, May.
    2. O. L. Mangasarian, 1985. "A Condition Number for Differentiable Convex Inequalities," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 175-179, May.
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