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The Pascoletti-Serafini scalarization scheme for multiobjective optimization problems

The nonlinear scalarization technique is an important approach to study nonconvex multiobjective optimization problems. At present, Pascoletti-Serafini scalarization scheme is one of the powerful tools to deal with nonconvex multiobjective optimization problems. However, most of these results are established for weak efficiency and efficiency to multiobjective optimization problems. Consequently, this paper is devoted to further investigation on the modifications of the Pascoletti-Serafini method, which are proposed by Akbari et al. (2018).We are interested in establishing relationships between (weakly, properly) efficient solutions of a general nonconvex multiobjective optimization problem and optimal solutions of the related scalarized problem under appropriate assumptions. For this purpose,necessary and sufficient conditions to (weakly, properly) efficient solutionsof a general nonconvex multiobjective optimization problem are achieved via restricting the ranges of the parameters involved in the corresponding scalarization problem.Furthermore, some examples are given to illustrate our main results.