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.
Tạp chí khoa học Trường Đại học Cần Thơ
Khu II, Đại học Cần Thơ, Đường 3/2, Phường Ninh Kiều, Thành phố Cần Thơ, Việt Nam
Điện thoại: (0292) 3 872 157; Email: tapchidhct@ctu.edu.vn
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