Perface: Special JOTA issue on “Variational Aspects of Vector Optimization”
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Vector or multi-objective optimization is concerned with making decisions to balance various conflicting objectives by virtue of Pareto efficiency via optimally distributing scarce resources. This model was initially proposed by W. Pareto in 19th century. Mature optimality theory has been established for vector optimization. There have been found many successful practical applications of vector optimization in economics and engineering.
Vector variational inequality problem was introduced by F. Giannessi in 1980. Comparing with vector optimization, this model does not imply the minimum (or maximum) of any functional. Extensive research on vector variational inequality problems has been carried out. Various properties of its solution set, such as nonemptiness, connectivity, and stability have been studied. The extension of this model includes vector complementarity problem, vector equilibrium problem, vector variational-like inequality problem, Minty vector variational inequality...