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Vector variational inequality as a tool for studying vector optimization problems. (English) Zbl 0956.49007
The aim of the paper is to show that the vector variational inequality (VVI) can be an efficient tool for studying vector optimization problems. It is shown that the necessary condition for a weak efficient point of a vector optimization problem with differentiable functions is a VVI. This observation suggests a way to use existing results on variational inequalities for vector optimization problems. Various basic facts on the class of strongly monotone VVI are established: Connectedness and compactness of the solution set. Furthermore, a Hölder-Lipschitz continuity property of the solution set of parametric problems is studied. From this result the authors derive interesting information about vector optimization problems with \(\varrho\)-convex functions. Finally, they discuss a useful example of a strongly monotone VVI whose solution set is not a singleton.

49J40 Variational inequalities
90C29 Multi-objective and goal programming
90C25 Convex programming
90C31 Sensitivity, stability, parametric optimization
Full Text: DOI
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