Abstract
For an inequality constrained nonsmooth multiobjective optimization problem involving locally Lipschitz functions, stronger KT-type necessary conditions and KT necessary conditions (which in the continuously differentiable case reduce respectively to the stronger KT conditions studied recently by Maeda and the usual KT conditions) are derived for efficiency and weak efficiency under several constraint qualifications. Stimulated by the stronger KT-type conditions, the notion of core of the convex hull of the union of finitely many convex sets is introduced. As main tool in the derivation of the necessary conditions, a theorem of the alternatives and a core separation theorem are also developed which are respectively extensions of the Motzkin transposition theorem and the Tucker theorem.
© 2000 Plenum Publishing Corporation
© 2000 Plenum Publishing Corporation
| Original language | English |
|---|---|
| Pages (from-to) | 373-398 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 106 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Aug 2000 |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
This work was supported by the National Natural Science Foundation of P.R. China.
Research Keywords
- Clarke subdifferential
- Constraint qualifications
- KT necessary conditions
- Lipschitz continuity
- Nonsmooth multiobjective optimization
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