New results on proper efficiency for a class of vector optimization problems

References

• Choo EU, Atkins DR. Bicriteria linear fractional programming. J Optim Theory Appl. 1982;36:203–220.
   Web of Science ®Google Scholar
• Choo EU, Atkins DR. Connectedness in multiple linear fractional programming. Manage Sci. 1983;29:250–255.
   Web of Science ®Google Scholar
• Steuer RE. Multiple criteria optimization: theory, computation and application. New York: John Wiley & Sons; 1986.
   Google Scholar
• Benoist J. Connectedness of the efficient set for strictly quasiconcave sets. J Optim Theory Appl. 1998;96:627–654.
   Web of Science ®Google Scholar
• Hoa TN, Huy NQ, Phuong TD, et al. Unbounded components in the solution sets of strictly quasiconcave vector maximization problems. J Global Optim. 2007;37:1–10.
   Web of Science ®Google Scholar
• Hoa TN, Phuong TD, Yen ND. Linear fractional vector optimization problems with many components in the solution sets. J Ind Manage Optim. 2005;1:477–486.
   Web of Science ®Google Scholar
• Hoa TN, Phuong TD, Yen ND. On the parametric affine variational inequality approach to linear fractional vector optimization problems. Vietnam J Math. 2005;33:477–489.
   Google Scholar
• Huong NTT, Yao J-C, Yen ND. Connectedness structure of the solution sets of vector variational inequalities. Optimization. 2017;66:889–901.
   Web of Science ®Google Scholar
• Huy NQ, Yen ND. Remarks on a conjecture of J. Benoist. Nonlinear Anal Forum. 2004;9:109–117.
   Google Scholar
• Lee GM, Tam NN, Yen ND. Quadratic programming and affine variational inequalities: a qualitative study. Vol. 78. New York: Springer Verlag; 2005. (Series: ‘Nonconvex Optimization and its Applications’).
   Google Scholar
• Malivert C. Multicriteria fractional programming. In: Sofonea M, Corvellec JN, editors. Proceedings of the 2nd Catalan Days on Applied Mathematics. Perpignan. Presses Universitaires de Perpinan; 1995. p. 189–198.
   Google Scholar
• Yen ND. Linear fractional and convex quadratic vector optimization problems. In: Ansari QH, Yao J-C, editors. Recent developments in vector optimization. Berlin: Springer Verlag; 2012. p. 297–328.
   Google Scholar
• Yen ND, Phuong TD. Connectedness and stability of the solution set in linear fractional vector optimization problems. In: Giannessi F, editor. Vector variational inequalities and vector equilibria. Dordrecht: Kluwer Academic Publishers; 2000. p. 479–489.
   Google Scholar
• Yen ND, Yao J-C. Monotone affine vector variational inequalities. Optimization. 2011;60:53–68.
   Web of Science ®Google Scholar
• Geoffrion AM. Proper efficiency and the theory of vector maximization. J Math Anal Appl. 1968;22:613–630.
   Web of Science ®Google Scholar
• Borwein JM. Proper efficient points for maximizations with respect to cones. SIAM J Control Optim. 1977;15:57–63.
   Web of Science ®Google Scholar
• Benson B. An improved definition of proper efficiency for vector maximization with respect to cones. J Math Anal Appl. 1979;71:232–241.
   Web of Science ®Google Scholar
• Henig MI. Proper efficiency with respect to cones. J Optim Theory Appl. 1982;36:387–407.
   Web of Science ®Google Scholar
• Sawaragi Y, Nakayama H, Tanino T. Theory of multiobjective optimization. New York: Academic Press; 1985.
   Google Scholar
• Huong NTT, Yao J-C, Yen ND. Geoffrion's proper efficiency in linear fractional vector optimization with unbounded constraint sets. Preprint 2018 (submitted).
   Google Scholar
• Choo EU. Proper efficiency and the linear fractional vector maximum problem. Oper Res. 1984;32:216–220. Available at http://www.jstor.org/stable/170530.
   Web of Science ®Google Scholar
• Huong NTT, Luan NN, Yen ND. The Borwein proper efficiency in linear fractional vector optimization. J Nonlinear Convex Anal. 2019; 20: 2579–2595.
   Web of Science ®Google Scholar
• Huong NTT, Wen C-F, Yao J-C, et al. Proper efficiency in linear fractional vector optimization via Benson's characterization. Preprint 2019 (submitted).
   Google Scholar
• Rockafellar RT. Convex analysis. Princeton, NJ: Princeton University Press; 1970.
   Google Scholar
• Luc DT. Theory of vector optimization. Berlin: Springer-Verlag; 1989.
   Google Scholar
• Luc DT. Multiobjective linear programming: an introduction. Cham: Springer; 2016.
   Google Scholar
• Lee GM, Yen ND. A result on vector variational inequalities with polyhedral constraints. J Optim Theory Appl. 2001;109:193–197.
   Web of Science ®Google Scholar
• Huong NTT, Yao J-C, Yen ND. Polynomial vector variational inequalities under polynomial constraints and applications. SIAM J Optim. 2016;26:1060–1071.
   Web of Science ®Google Scholar
• Kim DS, Pham TS, Tuyen NV. On the existence of Pareto solutions for polynomial vector optimization problems. Math Program A. 2019;177:321–341.
   Web of Science ®Google Scholar
• Hieu VT. An application of the Tarski–Seidenberg theorem with quantifiers to vector variational inequalities. Minimax Theory Appl.
   Google Scholar