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.


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
Full Text: EuDML