Vector approximation problems in geometric vector optimization

Using the geometric vector inequality, introduced by Elster-Elster-Göpfert, the authors consider a special case of that inequality which is a basis for treating certain classes of (nonsmooth) vector optimization problems: vector curve fitting problems, 𝓁p-vector approximation problems and vector regression problems. By the introduced geometric vector inequality they obtain in a natural way dual problems for such special-structured vector optimization problems, which can be solved in an efficient manner, since the dual constraints are linear.