Linear and Pascoletti–Serafini Scalarizations in Unified Set Optimization

This chapter is devoted to the study of linear and nonlinear scalarization schemes in unified set optimization in terms of approximate minimal solutions. Characterization of a preference set relation is employed to characterize approximate minimal solutions in terms of approximate minimal solutions of linearized scalar problems. Similar characterizations are derived using a nonlinear scalarization scheme, namely the Pascoletti–Serafini scalarization scheme for set optimization, which is an extension of the scheme considered in [Pascoletti, A., Serafini, P.: Scalarizing vector optimization problems, J. Optim. Theory Appl. 42(4), 499–524, 1984] for vector optimization problems.