Isolated Calmness in Regularized Convex Optimization

This paper studies the isolated calmness of the optimal solution mapping and the associated Lagrange system for regularized convex composite optimization problems. Several necessary and sufficient conditions for this property are established. These conditions are geometric in nature and relatively simple to verify. To support the analysis, we also develop a so-called zero-product property for second-order structures, namely the graphical derivative of the subgradient mapping of convex functions.