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Solution concepts in vector optimization: a fresh look at an old story
| Content Provider | Semantic Scholar |
|---|---|
| Author | Heyde, Frank Löhne, Andreas |
| Copyright Year | 2011 |
| Abstract | Over the past decades various solution concepts for vector optimization problems have been established and used: among them are efficient, weakly efficient and properly efficient solutions. In contrast to the classical approach, we define a solution to be a set of efficient solutions on which the infimum of the objective function with respect to an appropriate complete lattice (the space of self-infimal sets) is attained. The set of weakly efficient solutions is not considered to be a solution, but weak efficiency is essential in the construction of the complete lattice. In this way, two classic concepts are involved in a common approach. Several different notions of semicontinuity are compared. Using the space of self-infimal sets, we can show that various originally different concepts coincide. A Weierstrass existence result is proved for our solution concept. A slight relaxation of the solution concept yields a relationship to properly efficient solutions. |
| Starting Page | 1421 |
| Ending Page | 1440 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| DOI | 10.1080/02331931003665108 |
| Alternate Webpage(s) | http://sim.mathematik.uni-halle.de/reports/sources/2008/08-19report.pdf |
| Alternate Webpage(s) | http://ito.mathematik.uni-halle.de/~loehne/pdf/ewe_web.pdf |
| Alternate Webpage(s) | https://doi.org/10.1080/02331931003665108 |
| Volume Number | 60 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
