R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

Abstract The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example such a property set-valued mappings, whose graph set system inequalities and equations, R-regularity. Based on so-called relaxed constant positive linear dependence constraint qualification, we provide criterion ensuring R-regularity property. In this regard, our generalizes earlier results that type which exploited stronger Mangasarian–Fromovitz rank qualification. Afterwards, apply findings order to derive new sufficient conditions guarantee Finally, are used an existence solutions pessimistic condition partial calmness optimistic