|
|||||
|
|
An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets |
|
| Authors: | Yuto Ogata Tamaki Tanaka Yutaka Saito Gue Myung Lee Jae Hyoung Lee |
| Affiliation: | 1. Graduate School of Science and Technology, Niigata University , Niigata, Japan.y-ogata@m.sc.niigata-u.ac.jp;3. Graduate School of Science and Technology, Niigata University , Niigata, Japan.;4. Department of Management Science and Engineering, Akita Prefectural University , Yurihonjo, Japan.;5. Department of Applied Mathematics, Pukyong National University , Busan, Korea. |
| Abstract: | AbstractThis paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions. |
| Keywords: | Alternative theorem set-valued map set relation evaluation function robustness |