Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces

Authors:
Lucelina Batista dos Santos;Gabriel Ruiz-Garzón;Marko A. Rojas-Medar;Antonio Rufián-Lizana
Affiliations:
DM, Universidade Federal do Paraná, CP 19081, 81531-990, Curitiba-PR, Brazil;Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Facultad de Ciencias Sociales y de la Comunicación, Campus de Jerez de la Frontera, Cádiz, 114 ...;Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad de Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile;Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, 41012, Spain
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this work, 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 Ruiz-Garzon et al. [G. Ruiz-Garzon, R. Osuna-Gomez, A. Rufian-Lizana, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113-119].