On duality for mathematical programs with vanishing constraints

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

“…Moreover, it is also named "strongly stationary condition" (Hoheisel and Kanzow 2007;Kazemi and Kanzi 2018). The V C-S-stationary condition for differentiable scalar optimization problems with vanishing constraints can be found, for example, in Mishra et al (2016). Now, using the above concepts of stationary points, we formulate the necessary optimality conditions established in Theorems 13 and 15 in terms of the foregoing stationary points.…”

“…Because multiobjective optimization problems arise in different scientific applications, many researches have focused on developing optimality conditions B Tadeusz Antczak tadeusz.antczak@wmii.uni.lodz.pl 1 Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland and duality results for such mathematical programming problems and also methods for their solution. The available literature on optimality conditions and various types of duality for multiobjective programming problems is very rich (see, for example, several monographs on multiobjective programming which have been published in recent past, that is, Chen et al 2005;Chankong and Haimes 1983;Jahn 2004;Luc 1989;Miettinen 1999;Mishra et al 2016;Sawaragi et al 1985;Yu 1985).…”

“…Such an extremum problem has been recently introduced and studied by Achtziger and Kanzow (2008), motivated by several real-world applications, mainly for topology design problems in mechanical structures as described in their work. Since optimization problems with vanishing constraints, in their general form, are quite a new class of mathematical programming problems, very few works have only been published on this subject so far (see, for example, Achtziger et al 2013;Dorsch et al 2012;Dussault et al 2018;Guu et al 2017;Hoheisel and Kanzow 2007Hu et al 2019;Izmailov and Solodov 2009;Mishra et al 2015Mishra et al , 2016. Recently, Tung (2020) established the optimality and duality results for the considered multiobjective semi-infinite programming with vanishing constraints under convexity assumptions.…”

Karush-Kuhn-Tucker optimality conditions and duality for semi-infinite programming problems with vanishing constraints

“…The KKT necessary optimality conditions for mathematical programming problems with non-differentiable vanishing constraints were established in [14] via Clarke subdifferentials. Some results about duality for mathematical programming problems with vanishing constraints were obtained in [10,15]. On the other hand, an optimization with an infinite number of constraints is called a semi-infinite programming problem.…”

On nonsmooth mathematical programs with equilibrium constraints using generalized convexity

“…Wolfe [34], and Mond and Weir [27] dual models are most popular in nonlinear programming problems. Furthermore, these dual models have been abundantly studies for bilevel problems [33], semi-infinite programming problems [24], and mathematical programs with vanishing constraints (MPVC) [26].…”