Li, Shizheng On dual gap of semi-infinite programming. (Chinese. English summary) Zbl 0973.90081 Acta Math. Sci. (Chin. Ed.) 20, No. 1, 1-5 (2000). Summary: This paper proposes a dual problem \((D_1)\) for a semi-infinite convex programming problem (P). It is proved that a sufficient and necessary condition of no dual gap between \((D_1)\) and (P) is no dual gap between (P) and Lagrange’s dual problem (D) of (P). The saddle point criterion of (P) is a characterized by using the directional derivative. Cited in 1 Document MSC: 90C34 Semi-infinite programming 90C46 Optimality conditions and duality in mathematical programming 90C56 Derivative-free methods and methods using generalized derivatives Keywords:semi-infinite programming; dual problem; dual gap; directional derivative; subdifferential PDFBibTeX XMLCite \textit{S. Li}, Acta Math. Sci. (Chin. Ed.) 20, No. 1, 1--5 (2000; Zbl 0973.90081)