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 -