A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.
We present a filter trust region method for nonlinear semi-infinite programming. Based on the discretization technique and motivated by the multiobjective programming, we transform the semi-infinite problem into a finite one. Together with the filter technique, we propose a modified method that avoids the merit function. Compared with the existing methods, our method is more flexible and easier to implement. Under some mild conditions, the convergent properties are proved. Moreover, the numerical results are reported in the end.
Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vector programming problem are given in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066,2020). Having noticed inconsistencies in their paper, Gadhi and Ichatouhane (RAIRO-Oper. Res. doi:10.1051/ro/2020107, 2020) made the necessary corrections and proposed what they considered a more pertinent formulation of their main Theorem. Recently, Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020134) have criticised our work. This note is a critical response to this criticism.
In this paper, we establish sufficient Karush–Kuhn–Tucker (for short, KKT) conditions of a set-valued semi-infinite programming problem (SP) via the notion of contingent epiderivative of set-valued maps. We also derive duality results of Mond–Weir (MWD), Wolfe (WD), and mixed (MD) types of the problem (SP) under ρ-cone arcwise connectedness assumptions.
AbstractThe purpose of this paper is to study a nondifferentiable minimax semi-infinite programming problem in a complex space. For
such a semi-infinite programming problem, necessary and sufficient optimality conditions are established by utilizing the invexity assumptions. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. In order to relate the primal and dual problems, we have also derived appropriate duality theorems.
A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"
