Optimality and duality for proper and isolated efficiencies in multiobjective optimization |
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Institution: | 1. School of Economics and Management, China University of Geosciences, Wuhan 430074, China;2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China |
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Abstract: | 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 -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 -invexity-infineness hypotheses. |
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