Nonlinear Analysis: Theory, Methods & Applications
Calmness of constraint systems with applications
Mathematical Programming: Series A and B
Optimality Conditions for D.C. Vector Optimization Problems Under Reverse Convex Constraints
Journal of Global Optimization
Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
SIAM Journal on Optimization
Enhanced metric regularity and Lipschitzian properties of variational systems
Journal of Global Optimization
Second-order differentiability of generalized perturbation maps
Journal of Global Optimization
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In this paper we give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second-order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. An application to a special type of vector optimization problems, where the objective is given as the sum of two multifunctions, is presented. Furthermore, also as application, a special attention is paid for the case of perturbation set-valued maps which naturally appear in optimization problems.