%0 Journal Article
%A Thi Hong Diem, Huynh
%T Variational Approximations of a Dual Pair of Mathematical Programming Problems
%J Mathematical Analysis and Convex Optimization
%V 1
%N 1
%U http://maco.lu.ac.ir/article-1-49-en.html
%R 10.29252/maco.1.1.11
%D 2020
%K Variational approximations, mathematical programming, epi/hypo-convergence, inside epi/hypo-convergence, ancillary tightness, Lagrange functions, strong duality, approximate saddle points, approximate minsup-points, approximate maxinf-points,
%X We study variational approximations of a dual pair of mathematical programming problems in terms of epi/hypo-convergence and inside epi/hypo-convergence of approximating Lagrange functions of the pair. First, the Painlevé -Kuratowski convergence of approximate saddle points of approximating Lagrange functions is established under the inside epi/hypo-convergence of these approximating Lagrange functions. From this, we obtain a couple of solutions of the pair of problems and a strong duality. Under a stronger variational convergence called ancillary tight epi/hypo-convergence, we obtain the Painle vé-Kuratowski convergence of approximate minsup-points and approximate maxinf-points of approximating Lagrange functions (when approximate saddle points are not necessary to exist).
%> http://maco.lu.ac.ir/article-1-49-en.pdf
%P 107-118
%& 107
%!
%9 Research Article
%L A-10-62-1
%+ Hochiminh City University Of Technology
%G eng
%@ 2717-0624
%[ 2020