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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:
49K40Sensitivity, stability, well-posedness of optimal solutions
90C29Multi-objective programming; goal programming
47J20Inequalities involving nonlinear operators
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