This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure.

In this paper, we consider minimization problems with a quasiconvex vector-valued inequality constraint. We propose two constraint qualifications, the closed cone constraint qualification for vector-valued quasiconvex programming (the VQ-CCCQ) and the basic constraint qualification for vector-valued quasiconvex programming (the VQ-BCQ). Based on previous results by Benoist, Borwein, and Popovic...

In this paper, we introduce a constant positive linear dependence condition (CPLD), which is weaker than the Mangasarian–Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). We show that a limit point of a sequence of approximating Karush–Kuhn–Tucker (KKT) points is a KKT point if the CPLD holds there. We show that a KKT point satisfying the CPLD and ...

Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...

In this paper we study nonlinear programming problems with equality, inequality, and abstract constraints where some of the functions are Fréchet differentiable at the optimal solution, some of the functions are Lipschitz near the optimal solution, and the abstract constraint set may be nonconvex. We derive Fritz John type and Karush–Kuhn–Tucker (KKT) type first order necessary optimality condi...

The Constant Positive Linear Dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei and used for the analysis of SQP methods. In the paper where the CPLD was introduced, the authors conjectured that this condition could be a constraint qualification. This conjecture is proved in the present paper. Moreover, it will be shown that the CPLD c...

This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formula...