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Global optimality conditions for some classes of polynomial integer programming problems. (English) Zbl 1214.90089

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.

MSC:

90C10 Integer programming
90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
26C05 Real polynomials: analytic properties, etc.
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