A nonlinear scalarization function and generalized quasi-vector equilibrium problems.

*(English)*Zbl 1130.90413Summary: Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems.

##### MSC:

90C47 | Minimax problems in mathematical programming |

46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |

90C29 | Multi-objective and goal programming |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

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\textit{G. Y. Chen} et al., J. Glob. Optim. 32, No. 4, 451--466 (2005; Zbl 1130.90413)

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##### References:

[10] | Gerth(Tammer), Chr. and Weidner, P. (1990), Nonconvex secparation theorems and some applications in vector optimization, Journal of Optimization Theory and Applcaiotns, 67, 297–320. · Zbl 0692.90063 |

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