Duality related to approximate proper solutions of vector optimization problems
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DOI: 10.1007/s10898-015-0366-4
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- X. M. Yang & D. Li & S. Y. Wang, 2001. "Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 413-427, August.
- Z. F. Li, 1998. "Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 623-649, September.
- C. Gutiérrez & B. Jiménez & V. Novo, 2006. "On Approximate Efficiency in Multiobjective Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 165-185, August.
- T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
- ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
- C. Gutiérrez & B. Jiménez & V. Novo, 2011. "A generic approach to approximate efficiency and applications to vector optimization with set-valued maps," Journal of Global Optimization, Springer, vol. 49(2), pages 313-342, February.
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- Christian Günther & Bahareh Khazayel & Christiane Tammer, 2022. "Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 408-442, June.
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More about this item
Keywords
Vector optimization; Approximate duality; Proper $$varepsilon $$ ε -efficiency; Nearly cone-subconvexlikeness; Linear scalarization; 90C48; 90C25; 90C46; 49N15;All these keywords.
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