Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4632209 | Applied Mathematics and Computation | 2010 | 8 Pages |
Abstract
In this paper, we consider constrained optimization problems with set-valued objective maps. First, we define three types of quasi orderings on the set of all non-empty subsets in n-dimensional Euclidean space and investigate their properties. Next, by using these orderings, we define the concepts of the convexities to set-valued maps and investigate their properties. Finally, based on these results, we define the concepts of optimal solutions to constrained optimization problems with set-valued objective maps and characterize their properties.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Takashi Maeda,