On second-order optimality conditions for $C^{1,1}$ optimization problems via Lagrangian functions

This paper focuses on optimality conditions for $C^{1,1}$-smooth optimization problems subject to inequality and equality constraints. By employing the concept of limiting (Mordukhovich) second-order subdifferentials to the Lagrangian function associated with the problem, we derive new second-order optimality conditions for the considered problem. Applications for multiobjective optimization problems are studied as well. These results extend and refine existing results in the literature.