Mathematical Programming: Series A and B
Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities
SIAM Journal on Optimization
On Constraint Qualification for an Infinite System of Convex Inequalities in a Banach Space
SIAM Journal on Optimization
Equilibrium conditions and vector variational inequalities: a complex relation
Journal of Global Optimization
SIAM Journal on Optimization
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications
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In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite-dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half-spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite-dimensional vector optimization, specially with the Kurcyuscz-Robinson-Zowe constraint qualification, are also given.