Characterizations for Strong Abadie Constraint Qualification and Applications to Calmness

Zhou Wei (), Christiane Tammer () and Jen-Chih Yao ()
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Zhou Wei: Yunnan University
Christiane Tammer: Martin-Luther-University Halle-Wittenberg
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 1, No 1, 18 pages

Abstract: Abstract In this paper, we mainly study the Abadie constraint qualification (ACQ) and the strong ACQ of a convex multifunction. To characterize the general difference between strong ACQ and ACQ, we prove that the strong ACQ is essentially equivalent to the ACQ plus the finite distance of two image sets of the tangent derivative multifunction on the sphere and the origin, respectively. This characterization for the strong ACQ is used to provide the exact calmness modulus of a convex multifunction. Finally, we apply these results to local and global error bounds for a convex inequality defined by a proper convex function. The characterization of the strong ACQ enables us to give primal equivalent criteria for local and global error bounds in terms of contingent cones and directional derivatives.

Keywords: Strong Abadie constraint qualification; Abadie constraint qualification; Convex multifunction; Calmness; Error bounds; 90C25; 90C31; 49J53 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-020-01808-5

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