  


Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear SecondOrder Cone Programming
Roberto Andreani (andreaniunicamp.br) Abstract: In [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion of nondegeneracy (or transversality) and Robinson's constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely, its eigendecomposition. This allows formulating the conditions equivalently in terms of (positive) linear independence of significantly smaller sets of vectors. In this paper we extend these ideas to the context of nonlinear secondorder cone programming. For instance, for an mdimensional secondorder cone, instead of stating nondegeneracy at the vertex as the linear independence of m derivative vectors, we do it in terms of several statements of linear independence of 2 derivative vectors. This allows embedding the structure of the secondorder cone into the formulation of nondegeneracy and, by extension, Robinson's constraint qualification as well. This point of view is shown to be crucial in defining significantly weaker constraint qualifications such as the constant rank constraint qualification and the constant positive linear dependence condition. Also, these conditions are shown to be sufficient for guaranteeing global convergence of several algorithms, while still implying metric subregularity and without requiring boundedness of the set of Lagrange multipliers. Keywords: Secondorder cone programming, Constraint qualifications, Algorithms, Global convergence, Constant rank Category 1: Linear, Cone and Semidefinite Programming (SecondOrder Cone Programming ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF] Entry Submitted: 10/22/2021 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  