On solving parametric multiobjective quadratic programs with parameters in general locations

While theoretical studies on parametric multiobjective programs (mpMOPs) have been steadily progressing, the algorithmic development has been comparatively limited despite the fact that parametric optimization can provide a complete parametric description of the efficient set. This paper puts forward the premise that parametrization of the efficient set of nonparametric MOPs can be combined with solving parametric MOPs because the algorithms performing the former can also be used to achieve the latter.This strategy is realized through (i) development of a generalized scalarization, (ii) a computational study of selected parametric optimization algorithms, and (iii) applications in a real-life context. Several variants of a generalized weighted-sum scalarization allow one to scalarize mpMOPs to match the capabilities of algorithms. Parametric multiobjective quadratic programs are scalarized into parametric quadratic programs (mpQPs) with linear and/or quadratic constraints. In the computational study, three algorithms capable of solving mpQPs are examined on synthetic instances and two of the algorithms are applied to decision-making problems in statistics and portfolio optimization. The real-life context reveals the interplay between the scalarizations and provides additional insight into the obtained parametric solution sets.