Abstract
In this paper, we consider of finding efficient solution and weakly efficient solution for nonconvex vector optimization problems. When X and Y are normed spaces, F is an anti-Lipschitz mapping from X to Y, and the ordering cone is regular, we present an algorithm to guarantee that the generated sequence converges to an efficient solution with respect to normed topology. If the domain of the mapping is compact, we prove that the generated sequence converges to an efficient solution with respect to normed topology without requiring that mapping is anti-Lipschitz. We also give an algorithm to guarantee that the generated sequence converges to a weakly efficient solution with respect to normed topology.
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Communicated by Anton Abdulbasah Kamil.
This research was partially supported by the National Natural Science Foundation of China (11061023, 11201216, 11471291).
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Gong, XH., Liu, F. An Algorithm for Vector Optimization Problems. Bull. Malays. Math. Sci. Soc. 40, 919–929 (2017). https://doi.org/10.1007/s40840-017-0455-2
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DOI: https://doi.org/10.1007/s40840-017-0455-2