## 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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### References:

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