Variational Approximations of a Dual Pair of Mathematical Programming Problems

Document Type : Original Article

Author
Huynh Thi Hong Diem
Department of Applied Mathematics, University of Technology, Ho Chi Minh City, Vietnam
10.29252/maco.1.1.11
Abstract
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).

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 1
June 2020
Pages 107-118