Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming

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 discus...

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Bibliographic Details
Published in:Optimization letters 2022-03, Vol.16 (2), p.589-610
Main Authors: Andreani, R., Haeser, G., Mito, L. M., Ramírez, H., Santos, D. O., Silveira, T. P.
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
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Summary: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.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01737-w