Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints

In this paper, we establish some general metric regularity results for multivalued functions on Banach spaces. Then, we apply them to derive second-order necessary optimality conditions for the problem of minimizing a functionf on the solution set of an inclusion 0F(x) withxC, whenF has a closed convex second-order derivative.The author is thankful to the referees for having helped him improve the quality of the paper.