Sufficient conditions for error bounds of difference functions and applications

Nguyen Thi Hang () and Jen-Chih Yao ()
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Nguyen Thi Hang: Vietnam Academy of Science and Technology
Jen-Chih Yao: China Medical University

Journal of Global Optimization, 2016, vol. 66, issue 3, No 4, 439-456

Abstract: 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.

Keywords: d.c. inequalities system; Error bounds; Subdifferential; Exact penalty function; Lagrange multipliers; 49J52; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10898-016-0410-z

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