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Sufficient conditions for error bounds of difference functions and applications

Author

Listed:
  • Nguyen Thi Hang

    (Vietnam Academy of Science and Technology)

  • Jen-Chih Yao

    (China Medical University)

Abstract

This paper establishes verifiable sufficient conditions for the existence of error bounds for the sub-level set of a difference function over an abstract constraint by applying a technique used by A. D. Ioffe. As a consequence, error bounds for constraint systems defined by d.c. inequalities and their applications in studying of exactness of the associated $$\ell _1$$ ℓ 1 penalty function and existence of Lagrange multipliers as necessary optimality conditions are also investigated.

Suggested Citation

  • Nguyen Thi Hang & Jen-Chih Yao, 2016. "Sufficient conditions for error bounds of difference functions and applications," Journal of Global Optimization, Springer, vol. 66(3), pages 439-456, November.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:3:d:10.1007_s10898-016-0410-z
    DOI: 10.1007/s10898-016-0410-z
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    References listed on IDEAS

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    1. A. A. Auslender & J.-P. Crouzeix, 1988. "Global Regularity Theorems," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 243-253, 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.
    3. Hoai Le Thi & Tao Pham Dinh & Huynh Ngai, 2012. "Exact penalty and error bounds in DC programming," Journal of Global Optimization, Springer, vol. 52(3), pages 509-535, March.
    4. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
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