On vector variational E-inequalities and differentiable vector optimization problem

Tadeusz Antczak () and Najeeb Abdulaleem ()
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Tadeusz Antczak: University of Łódź
Najeeb Abdulaleem: University of Łódź

OPSEARCH, 2024, vol. 61, issue 1, No 21, 460-482

Abstract: Abstract In this paper, in order to characterize optimality of a class of nonconvex differentiable multiobjective programming problems, we introduce two new types of vector variational-like inequalities, namely, a weak variational E-inequality and a vector variational E-inequality. Namely, under (strictly) E-convexity, we prove relationships between the aforesaid vector variational-like inequalities and differentiable vector optimization problems. Further, under (strictly) pseudo-E-convexity, we are in position to identify vector critical E-points, weak E-Pareto (E-Pareto) solutions of differentiable vector optimization problems and solutions of these introduced vector variational-like inequalities.

Keywords: (Weak) vector variational E-inequality; (Weak) differentiable vector optimization problem; Vector critical E-point; E-convex function; Pseudo-E-convex function; 90C33; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s12597-023-00698-1

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