Abstract
In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.
Original language | English |
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Pages (from-to) | 1243-1256 |
Number of pages | 14 |
Journal | Science in China, Series A: Mathematics |
Volume | 51 |
Issue number | 7 |
DOIs | |
Publication status | Published - 1 Jul 2008 |
Keywords
- Connectedness
- Normed space
- Piecewise linear function
- Weak Pareto solution
ASJC Scopus subject areas
- General Mathematics