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

  • Authors:

  • Gabriel Ruiz-Garzón;Lucelina Batista dos Santos;Antonio Rufián-Lizana;Manuel Arana-Jiménez

  • Affiliations:

  • Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Facultad de Ciencias Sociales y de la Comunicación, Campus de Jerez de la Frontera, E-11405 Cá ...;DM, Universidade Federal do Paraná, CP 19081, 81531-990, Curitiba-PR, Brazil;Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Facultad de Matemáticas, E-41012 Sevilla, Spain;Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Escuela Superior de Ingeniería, E-11002 Cádiz, Spain

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach spaces under pseudo-invexity and pseudo-monotonicity hypotheses. We have extended the results given by Gang and Liu (2008) [22] to Banach spaces and the relationships obtained for weak efficient points in Santos et al. (2008) [21] are completed and enabled to relate vector critical points, weak efficient points, solutions of the Minty and Stampacchia weak vector variational-like inequalities problems and solutions of perturbed vector variational-like inequalities problems.