Batista Dos Santos, Lucelina; Ruiz-Garzón, Gabriel; Rojas-Medar, Marko A.; Rufián-Lizana, Antonio Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces. (English) Zbl 1138.49010 Comput. Math. Appl. 55, No. 8, 1808-1814 (2008). Summary: We will establish some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces under invexity hypotheses. This paper extends the earlier work of G. Ruiz-Garzón, R. Osuna-Gómez and A. Rufián-Lizana [Eur. J. Oper. Res. 157, No. 1, 113–119 (2004; Zbl 1106.90060)]. Cited in 9 Documents MSC: 49J40 Variational inequalities 90C26 Nonconvex programming, global optimization Keywords:vectorial optimization problem; variational-like inequality problem; weak efficiency; Banach spaces; pseudoinvex functions Citations:Zbl 1106.90060 PDF BibTeX XML Cite \textit{L. Batista Dos Santos} et al., Comput. Math. Appl. 55, No. 8, 1808--1814 (2008; Zbl 1138.49010) Full Text: DOI OpenURL References: [1] Dafermos, S., Exchange price equilibrium and variational inequalities, Math. program., 46, 391-402, (1990) · Zbl 0709.90013 [2] Harker, P.T.; Pang, J.S., Finite dimensional variational inequality and nonlinear complementarity problems: a survey of theory, Math. program., 48, 161-220, (1990) · Zbl 0734.90098 [3] Kinderlehrer, D.; Stampacchia, G., An introduction to variational inequalities and their applications, (1980), Academic Press London · Zbl 0457.35001 [4] Mancino, O.G.; Stampacchia, G., Convex programming and variational inequalities, J. optim. theory appl., 9, 3-23, (1972) · Zbl 0213.45202 [5] Parida, J.; Sahoo, M.; Kumar, A., A variational-like inequality problem, Bull. austral. math. soc., 39, 225-231, (1989) · Zbl 0649.49007 [6] Ruiz-Garzón, G.; Osuna-Gómez, R.; Rufián-Lizana, A., Generalized invex monotonicity, European J. oper. res., 144, 501-512, (2003) · Zbl 1028.90036 [7] Ruiz-Garzón, G.; Osuna-Gómez, R.; Rufián-Lizana, A., Relationships between vector variational-like inequality and optimization problems, European J. oper. res., 157, 113-119, (2004) · Zbl 1106.90060 [8] Mishra, S.K.; Noor, M.A., On vector variational-like inequality problems, J. math. anal. appl., 311, 69-75, (2005) · Zbl 1078.49007 [9] Mishra, S.K.; Wang, S.Y., Vector variational-like inequalities and non-smooth vector optimization problems, Nonlinear anal., 64, 1939-1945, (2006) · Zbl 1134.49003 [10] Yang, X.Q.; Goh, C.J., On vector variational inequalities: application to vector equilibria, J. optim. theory appl., 95, 431-443, (1997) · Zbl 0892.90158 [11] Lee, G.M.; Kum, S., (), 307-320 [12] Ansari, Q.H.; Siddiqi, A.H., A generalized vector variational-like inequality and optimization over a efficient set, (), 177-191 · Zbl 0906.49005 [13] Kazmi, K.R., Some remarks on vector optimization problems, J. optim. theory appl., 96, 133-138, (1998) · Zbl 0897.90166 [14] Yang, X.Q., (), 423-432 [15] Flett, T.M., () [16] Osuna-Gómez, R.; Rufián-Lizana, A.; Ruiz-Canales, P., Invex functions and generalized convexity in multiobjective programming, J. optim. theory appl., 98, 651-661, (1998) · Zbl 0921.90133 [17] Craven, B.D., Lagrangean conditions and quasiduality, Bull. austral. math. soc., 16, 325-339, (1977) · Zbl 0362.90106 [18] Craven, B.D., Mathematical programming and control theory, (1978), Chapman and Hall · Zbl 0431.90039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.