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Stable and total Fenchel duality for DC optimization problems in locally convex spaces. (English) Zbl 1236.90140
The authors study an unconstrained minimization problem in which the objective function is of the form \(f(x) + g(Ax)\), where \(f, g\) are DC functions defined on locally convex spaces \(X\) and \(Y\), respectively, \(A: X\rightarrow Y\), and introduce two types of Fenchel dual problems for it. Some constraint qualifications are considered to establish weak duality theorems and strong duality theorems among which are results on the strong Fenchel duality, the stable Fenchel duality and the stable total duality.
Reviewer: Do Van Luu (Hanoi)

MSC:
90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)
90C26 Nonconvex programming, global optimization
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