Constant rank-type constraint qualifications and second-order optimality conditions

The Constant Rank Constraint Qualification (CRCQ), introduced by Janin in [Math. Program. Study 21:110-126, 1984], has several applications in nonlinear programming context, such as computing the derivative of the value function, second-order optimality conditions, global convergence, stability analysis and encompass without entirely the linear program problems. This work will present an extension of CRCQ that retrieves the well known properties from nonlinear programming and, in addition, to propose a constraint qualification based on curves that naturally rises from CRCQ and explain in a very simple way the second-order optimality conditions that can be obtained for second-order cone programming problems.