First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition

The well known constant rank constraint qualification [Math. Program. Study 21:110–126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context exploiting the eigenvector structure of problem. In this paper we propose more general and geometric approach defining new extension condition context. main advantage our is that are able recast strong second-order properties in particular, obtain necessary optimality stronger than classical one obtained under Robinson’s qualification, sense it holds every Lagrange multiplier, even though independent condition.