Quan, Jing; Wu, Zhiyou; Li, Guoquan Global optimality conditions for some classes of polynomial integer programming problems. (English) Zbl 1214.90089 J. Ind. Manag. Optim. 7, No. 1, 67-78 (2011). Summary: Ssome verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity. Cited in 2 Documents MSC: 90C10 Integer programming 90C46 Optimality conditions and duality in mathematical programming 90C26 Nonconvex programming, global optimization 26C05 Real polynomials: analytic properties, etc. Keywords:global optimality conditions; polynomial integer programming problem; abstract convexity PDFBibTeX XMLCite \textit{J. Quan} et al., J. Ind. Manag. Optim. 7, No. 1, 67--78 (2011; Zbl 1214.90089) Full Text: DOI