Abstract
Previous theoretical work in multiple-objective optimization has focused entirely on vector orders representable by positive cones. Here, we treat multiple-objective problems in which solutions are sought which are maximal (efficient, nondominated) under an order which may be nonconical. Compactness conditions under which maximal solutions exist and bound the remaining alternatives are given. First-order necessary conditions and first-order sufficient conditions for maximality in general normed linear spaces are derived, and a scalarization result is given. A small computational example is also presented. Several previous results are special cases of those given here.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 25-60 |
| Number of pages | 36 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 40 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1 1983 |
Keywords
- Multiple-objective optimization
- existence theorems
- first-order optimality conditions
- normed linear spaces
- vector optimization
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics