Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming
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 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.
Keywords
Cite
@article{arxiv.2008.07894,
title = {Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming},
author = {R. Andreani and G. Haeser and L. M. Mito and H. Ramirez and D. O. Santos and T. P. Silveira},
journal= {arXiv preprint arXiv:2008.07894},
year = {2020}
}
Comments
An older version of this paper was separated in two, and SDP was included here. The first part can be found here: https://www.ime.usp.br/~ghaeser/nota-crcq-errata.pdf