Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives

P. Q. Khanh () and N. D. Tuan
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P. Q. Khanh: International University of Hochiminh City
N. D. Tuan: University of Natural Sciences of Hochiminh City

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 3, No 5, 357 pages

Abstract: Abstract We establish both necessary and sufficient optimality conditions for weak efficiency and firm efficiency by using Hadamard directional derivatives and scalarizing the multiobjective problem under consideration via signed distances. For the first-order conditions, the data of the problem need not even be continuous; for the second-order conditions, we assume only that the first-order derivatives of the data are calm. We include examples showing the advantages of our results over some recent papers in the literature.

Keywords: Multiobjective optimization; Weak efficiency; Firm efficiency; Signed distances; Hadamard directional derivatives; Calmness (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-007-9169-1

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