Journal of Optimization Theory and Applications

, Volume 171, Issue 1, pp 228–250 | Cite as

Error Bounds Via Exact Penalization with Applications to Concave and Quadratic Systems

  • Hoai An Le Thi
  • Huynh Van Ngai
  • Tao Pham Dinh


In this paper, we deal with the error bounds for inequality systems and the exact penalization for constrained optimization problems. We firstly investigate the relationships between the error bound and the exact penalization. Then we establish the new error bounds for inequality systems of concave functions and of nonconvex quadratic functions over polyhedral convex sets.


Subdifferential Exact penalty Error bound Concave Quadratic 

Mathematics Subject Classification

49J52 90C26 90C30 90C31 



We would like to thank the referees for their helpful comments and suggestions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Hoai An Le Thi
    • 1
  • Huynh Van Ngai
    • 2
  • Tao Pham Dinh
    • 3
  1. 1.Laboratoiry of Theoretical and Applied Computer ScienceUniversité de LorraineMetzFrance
  2. 2.Department of MathematicsUniversity of QuynhonQui NhonVietnam
  3. 3.Laboratory of MathematicsINSA-Rouen, University of NormandieSaint-Étienne-du-Rouvray CedexFrance

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