Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming

In Andreani et al. (Weak notions of nondegeneracy in nonlinear semidefinite programming, 2020), the classical notion (or transversality) and Robinson’s constraint qualification have been revisited context programming exploiting structure problem, namely its eigendecomposition. This allows formulating conditions equivalently terms (positive) linear independence significantly smaller sets vectors. this paper, we extend these ideas to second-order cone programming. For instance, for an m-dimensional cone, instead stating at vertex as m derivative vectors, do it several statements 2 embedding into formulation and, by extension, well. point view is shown be crucial defining weaker qualifications such constant rank positive dependence condition. Also, are sufficient guaranteeing global convergence algorithms, while still implying metric subregularity without requiring boundedness set Lagrange multipliers.