Weak sharp minima for semi-infinite optimization problems with applications

We study local weak sharp minima and sharp minima for smooth semi- infinite optimization problems SIP. We provide several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum of SIP. As applications, we present several sufficient and necessary conditions of calmness for infinitely many smooth inequalities. In particular, we improve some calmness results in [ R. Henrion and J. Outrata, Math. Program., 104 ( 2005), pp. 437 - 464].