TY - JOUR T1 - Variational Approximations of a Dual Pair of Mathematical Programming Problems TT - JF - lu-maco JO - lu-maco VL - 1 IS - 1 UR - http://maco.lu.ac.ir/article-1-49-en.html Y1 - 2020 SP - 107 EP - 118 KW - Variational approximations KW - mathematical programming KW - epi/hypo-convergence KW - inside epi/hypo-convergence KW - ancillary tightness KW - Lagrange functions KW - strong duality KW - approximate saddle points KW - approximate minsup-points KW - approximate maxinf-points N2 - 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). M3 10.29252/maco.1.1.11 ER -