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Optimality conditions and Toland’s duality for a nonconvex minimization problem. (English) Zbl 1051.49020

The author considers necessary and sufficient conditions and provides duality theory for a wide class of problems arising in nonconvex optimization, such as minimizing a difference of two convex functions subject to a convex vector constraint taking values in an ordered topological vector space. These results are then used to study a problem of nondifferentiable optimization.

MSC:

49N15 Duality theory (optimization)
49K27 Optimality conditions for problems in abstract spaces
90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
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