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Weak sharp minima for semi-infinite optimization problems with applications. (English) Zbl 1190.90251
Summary: 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 of R. Henrion and J. Outrata [Math. Program. 104, No. 2–3 (B), 437–464 (2005; Zbl 1093.90058)].
90C34Semi-infinite programming
90C30Nonlinear programming
49J52Nonsmooth analysis (other weak concepts of optimality)
65K10Optimization techniques (numerical methods)