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Optimality and duality for proper and isolated efficiencies in multiobjective optimization. (English) Zbl 1252.49018

Summary: We use some advanced tools of variational analysis and generalized differentiation such as the nonsmooth version of Fermat’s rule, the limiting/Mordukhovich subdifferential of maximum functions, and the sum rules for the Fréchet subdifferential and for the limiting one to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multiobjective optimization problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also provided under assumptions of (local) convex/affine functions or \(L\)-invex-infine functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problems and examine weak/strong duality relations under \(L\)-invexity-infineness hypotheses.

MSC:

49J52 Nonsmooth analysis
49K99 Optimality conditions
49N15 Duality theory (optimization)
65K10 Numerical optimization and variational techniques
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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