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On generalized derivatives for \(C^{1,1}\) vector optimization problems. (English) Zbl 1023.90058

Summary: We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involving \(C^{1,1}\) data. We show that these conditions are stronger than those in literature obtained by means of second-order Clarke subdifferential.

MSC:

90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
26B25 Convexity of real functions of several variables, generalizations
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
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