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.


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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