Henig globally efficiency for set-valued optimization and vector variational inequality

Weir T and Mond B, Preinvex functions in multiple-objective optimization, Journal of Mathematical Analysis and Applications, 1988, 136: 29–38. Bhatiaa D and Mehra A, Lagrangian duality for preinvex set-valued functions, Journal of Mathematical Analysis and Applications, 1997, 214(2): 599–612. Mishra S K, Giorgi G, and Wang S Y, Duality in vector optimization in Banach spaces with generalized convexity, Journal of Global Optimization, 2004, 29: 415–424. Noor M A, On generalized preinvex functions and monotonicities, J. Inequal. Pure Appl. Math., 2004, 5(4): 1–9. Jabarootian T and Zafarani J, Characterizations of preinvex and prequasiinvex set-valued maps, Taiwanese Journal of Mathematics, 2009, 113(3): 871–898. Yu G L and Liu S Y, Some vector optimization problems in Banach spaces with generalized convexity, Computers and Mathematics with Applications, 2007, 54: 1403–1410. Yu G L, Directional derivatives and generalized preinvex set-valued optimization, Acta Mathematica Sinica, 2011, 54(5): 705–880. Qiu J H, Cone-directed contingent derivatives and generalized preinvex set-valued optimization, Acta Mathematica Scientia, 2007, 27B(1): 211–218. Borwein J M and Zhuang D M, Super efficiency in vector optimization, Trans. Amer. Math. Soc., 1993, 338: 105–122. Benson H P, An improved definition of proper efficiency for vector maximization with respect to cones, Journal of Mathematical Analysis and Applications, 1979, 71: 232–241. Henig M I, Proper efficiency with respect to cones, Journal of Optimization Theory and Applications, 1982, 36: 387–407. Gong X H, Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior, Journal of Mathematical Analysis and Applications, 2005, 307: 12–31. Gong X H, Dong H B, and Wang S Y, Optimality conditions for proper efficient solutions of vector set-valued optimization, Journal of Mathematical Analysis and Applications, 2003, 284: 332–350. Yu G L and Liu S Y, Optimality conditions of globally proper efficient solutions for set-valued optimization problem, Acta Mathematica Applicatae Sinica (Chinese Series), 2010, 33(1): 150–160. Yu G L and Liu S Y, Globally proper saddle point in ic-cone-convexlike set-valued optimization problems, Acta Mathematica Sinica (English Series), 2009, 25(11): 1921–1928. Giannessi F, Variational Inequalities and Complementarity Problems, Wiley, New York, 1980. Noor M A, Preinvex functions and variational inequalities, J. Nat. Geometry, 1996, 9: 63–76. Khan M F, On generalized vector variational-like inequalities, Nonlinear Anal., 2004, 59: 879–889. Ruiz-Garzon G, Osuna-Gomez R, and Rufian-Lizana A, Relationships between vector variationallike inequality and optimization problems, Eur. J. Oper. Res., 2004, 157: 113–119. Fang Y P and Huang N J, Variational-like inequalities with generalized monotone mappings in Banach spaces, J. Optim. Theory Appl., 2003, 118: 327–338. Liu W and Gong X H, Proper efficiency for set-valued vector optimization problems and vector variational inequalites, Mathematical Methods of Operations Research, 2000, 51: 443–457. Zeng J and Li S J, On vector variational-like inequalities and set-valued optimization problems, Optimization Letters, 2011, 5(1): 55–69. Rezaie M and Zafarani J, Vector optimization and variational-like inequalities, Journal of Global Optimization, 2009, 43(1): 47–66. Jahn J and Rauh R, Contingent epiderivatives and set-valued optimzation, Mathematical Methods of Operation Research, 1997, 46: 193–211. Jahn J and Rauh R, The existence of contingent epiderivatives for set-valued maps, Applied Mathematics Letters, 2003, 16(8): 1179–1185. Chen G Y and Jahn J, Optimality conditions for set-valued optimization problem, Mathematical Methods of Operation Research, 1998, 48: 187–200.