Calmness of Set-Valued Mappings Between Asplund Spaces and Application to Equilibrium Problems

The paper deals with the calmness of two classes of nonconvex set-valued mappings in Asplund spaces and its application to equilibrium problems. Its main part is devoted to establish new sufficient conditions for calmness, which are derived in terms of coderivatives and w* boundaries of normal cones to constraint sets. In order to achieve this goal, a new concept so-called “sequential normal smoothness” for the sets in Asplund spaces is introduced and compared with two well-known notions of convexity and semismoothness. Finally, the results are applied to prove necessary optimality conditions for nonparametric equilibrium problems under new weak constraint qualifications.