The aim of this work is to investigate optimization-related problems with the objective spaces or... more The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin–Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.
Journal of Industrial and Management Optimization, 2017
This paper considers the parametric primal and dual vector equilibrium problems in locally convex... more This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems. As applications, some new results for vector optimization problem and vector variational inequality are derived. Our results are new and improve the existing ones in the literature.
The aim of this work is to investigate optimization-related problems with the objective spaces or... more The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin–Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.
Journal of Industrial and Management Optimization, 2017
This paper considers the parametric primal and dual vector equilibrium problems in locally convex... more This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems. As applications, some new results for vector optimization problem and vector variational inequality are derived. Our results are new and improve the existing ones in the literature.
Uploads
Papers by Lam Quoc Anh