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**Well posedness in vector optimization problems and vector variational inequalities.**
*(English)*
Zbl 1119.49025

Summary: We give notions of well posedness for a vector optimization problem and a vector variational inequality of the differential type. First, the basic properties of well-posed vector optimization problems are studied and the case of \(C\)-quasiconvex problems is explored. Further, we investigate the links between the well posedness of a vector optimization problem and of a vector variational inequality. We show that, under the convexity of the objective function \(f\), the two notions coincide. These results extend properties which are well known in scalar optimization.

### MSC:

49K40 | Sensitivity, stability, well-posedness |

90C29 | Multi-objective and goal programming |

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

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\textit{G. P. Crespi} et al., J. Optim. Theory Appl. 132, No. 1, 213--226 (2007; Zbl 1119.49025)

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### References:

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