E-Benson proper efficiency in vector optimization

Unified vector quasiequilibrium problems via improvement sets and nonlinear scalarization with stability analysis

“…where ε > 0 and E is an improvement set with respect to C; (vi) intE, where E is a solid (i.e., intE = ∅) improvement set with respect to C. For more details and examples of improvement sets, one can refer to [23,14,39,40,41,33,28]. 3.…”

“…Gutiérrez et al [23] generalized the concepts of improvement set and E-optimality to a general topological vector space. Subsequent works about this aspect one can also refer to Zhao and Yang [39,40], Zhao et al [41], Oppezzi and Rossi [33], Lalitha and Chatterjee [28]. As mentioned in [23], E-optimality via improvement sets has been shown to be very suitable to deal in a unified way with well-known exact and approximate nondominated concepts.…”

Extensions of proper efficiency in complex space

“…Generalized treatments with applications, in this topic, exist in previous works. [6][7][8][9][10] On the other hand, complex mathematical programming problems were initially studied by Levinson,11 in a particular linear form. Henceforward, several topics of the optimization theory were extended to complex space (see Elbrolosy 12 for example).…”

ε‐Properly Efficiency of Multiobjective Semidefinite Programming with Set‐Valued Functions

“…Chicco et al [7] proposed a new type of solution based on the upper comprehensive sets and discussed the existence of optimal points in multicriteria situations. Zhao and Yang [8] obtained some useful properties of -Benson proper efficiency. Gutiérrez et al [9] presented some properties of strict efficient solutions in vector optimization related to the -efficiency notion.…”