A minimax theorem for vector-valued functions in lexicographic order

Relaxation of constraints in lexicographic multiobjective programming problems

“…Rentmeesters et al [15] demonstrated that solutions obtained by the lexicographic scalarization do not satisfy the typical constraint qualification of regularity associated with the K.K.T optimality conditions. Li et al [16] obtained a minmax theorem and a saddle point theorem for vector-valued functions in the sense of lexicographic order. Simplicity of the lexicographic approach attracts the attention of many researchers in many fields.…”

Minimax Problems of Uniformly Same-Order Set-Valued Mappings

“…Gong [11] established a strong minimax theorem and a strong cone saddle point theorem of vector-valued functions. Li et al [17] investigated a minimax theorem and a saddle point theorem for vector-valued functions in the sense of lexicographic order.…”

“…Zhang et al [28,29] obtained some minimax problems for general set-valued mappings by using some fixed point theorems. Motivated by earlier work [13,16,17,19,22,23,27], we introduce a class of set-valued mappings, which is called uniformly same-order. For this sort of mappings, we investigate some minimax problems without any hypotheses of convexity.…”

Ky Fan minimax inequalities for set-valued mappings

“…Gong [16] obtained a strong minimax theorem and established an equivalent relationship between the strong minimax inequality and a strong cone saddle point theorem for vector-valued functions. Li et al [17] investigated a minimax theorem and a saddle point theorem for vector-valued functions in the sense of lexicographic order, respectively.…”