Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. A new condition of this type is introduced in the present paper. It will be proved that ...

This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations; hence leading to new constraint qualifi...

We exhibit certain second-order regularity properties of parametric complementarity constraints, which are notorious for being irregular in the classical sense. Our approach leads to a constraint qualification in terms of 2-regularity of the mapping corresponding to the subset of constraints which must be satisfied as equalities around the given feasible point, while no qualification is require...

This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting real Hilbert spaces. The weak and strong convergence theorems introduced are presented under some constraint qualifications scalar sequences. discussions on numerical experiments also provided to demonstrate effectiveness proposed algorithms.

In this paper an inverse optimal control problem in the form of a mathematical program with complementarity constraints (MPCC) is considered and numerical experiences are discussed. The inverse optimal control problem arises in the context of human navigation where the body is modeled as a dynamical system and it is assumed that the motions are optimally controlled with respect to an unknown co...

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications introduce a weak qualification which assures the equivalence between SCAKKT Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483-500, 1994) problems.