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
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