Weak sharp minima for semi-infinite optimization problems with applications. (English) Zbl 1190.90251

Zheng, Xi Yin; Yang, Xiao Qi

SIAM J. Optim. 18, No. 2, 573-588 (2007).

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)].

MSC:

90C34	Semi-infinite programming
90C30	Nonlinear programming
49J52	Nonsmooth analysis
65K10	Numerical optimization and variational techniques

Keywords:

semi-infinite optimization; sharp minima; weak sharp minima; subdifferential; normal cone

Citations:

Zbl 1093.90058