Abstract
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualifications to second-order cone programming and semidefinite programming, which are based on the Approximate-Karush–Kuhn–Tucker necessary optimality condition and on the application of the reduction approach. Our definitions are strictly weaker than Robinson’s constraint qualification, and an application to the global convergence of an augmented Lagrangian algorithm is obtained.
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We would like to thank Ellen H. Fukuda (Kyoto University) and Paulo J.S. Silva (University of Campinas) for initial discussions on this topic. This work was supported by CEPID-CeMEAI (FAPESP 2013/07375-0), FAPESP (grants 2018/24293-0, 2017/18308-2, 2017/17840-2, and 2017/12187-9), CNPq (grants 301888/2017-5, 303427/2018-3, and 404656/2018-8), PRONEX - CNPq/FAPERJ (grant E-26/010.001247/2016), and FONDECYT grant 1201982 and Basal Program CMM-AFB 170001, both from ANID (Chile).
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Andreani, R., Haeser, G., Mito, L.M. et al. Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming. Optim Lett 16, 589–610 (2022). https://doi.org/10.1007/s11590-021-01737-w
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DOI: https://doi.org/10.1007/s11590-021-01737-w