Coradiant sets and \(\varepsilon \)-efficiency in multiobjective optimization
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This paper studies \(\varepsilon \)-efficiency in multiobjective optimization by using the so-called coradiant sets. Motivated by the nonlinear separation property for cones, a similar separation property for coradiant sets is investigated. A new notion, called Bishop–Phelps coradiant set is introduced and some appropriate properties of this set are studied. This paper also introduces the notions of \(\varepsilon \)-dual and augmented \(\varepsilon \)-dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for \(\varepsilon \)-efficient and proper \(\varepsilon \)-efficient points are proposed.
KeywordsMultiobjective optimization Efficiency \(\varepsilon \)-Efficiency Bishop and Phelps coradiant set Scalarization
- 9.Helbig, S.: On a New Concept for \(\varepsilon \)-Efficiency: talk at “Optimization Days 1992”, Montreal (1992)Google Scholar
- 14.Kasimbeyli, R., Kasimbeyli, N.: The nonlinear separation theorem and a representation theorem for Bishop Phelps Cones. In: Modelling, Computation and Optimization in Information Systems and Management Sciences. Springer International Publishing. 419–430 (2015)Google Scholar
- 22.Sayadi-Bander, A., Pourkarimi, L., Basirzadeh, H.: On Convex Coradiant Set. (under review)Google Scholar
- 25.Tanaka, T.: A new approach to approximation of solutions in vector optimization problems. In: Proceedings of APORS. World Scientific Publishing, Singapore, 497–504 (1995)Google Scholar