Weak Sharp Minima: Characterizations and Sufficient Conditions

Error Bounds: Necessary and Sufficient Conditions

“…In the context of an optimization problem minimize f (x) subject to x ∈ C, calmness of the multifunction y → {x ∈ C | f (x) ≤ y} at local solutions (or equivalently, metric subregularity of the inverse multifunction) amounts to these solutions being weak sharp local minimizers (see, e.g., [7,49]). …”

“…Its main idea has been used several times in various contexts (e.g. [25,45,49]) with various subdifferentials (Fréchet, limiting, outer). A different subdifferential criterion was obtained in [18,19] as a by-product in the investigation of calmness of a standard constraint system in the sense of [48].…”

Weak Sharp Minima for Semi-infinite Optimization Problems with Applications

“…Extensive study of weak sharp minima for real-valued convex functions has been done in the literature (cf. [2,3,28,31,33]). It has been found that the weak sharp minimum is closely related to the error bound in convex programming (cf.…”

Subsmooth semi-infinite and infinite optimization problems

“…Extensive study of weak sharp minima for real-valued convex functions has been done in the literature (cf. [4,5,31,34,35]). It has been found that the weak sharp minimum is closely related to the error bound in convex programming, a notion that has received much attention and has produced a vast number of publications (see [14,19,25,35,36] and references therein).…”