约束品性与非光滑多目标优化问题

Constraint qualification and nonsmooth multiobjective optimization probems

考虑带不等式和集约束的非光滑多目标优化问题。首先利用Clarke方向导数、切锥、可达方向锥和线性化锥等工具引入广义Abadie约束品性和广义Kuhn-Tucker约束品性。进一步,分别在广义Abadie约束品性成立和广义Kuhn-Tucker约束品性成立这两种情况下,证明了Geoffrion真有效解是广义Kuhn-Tucker真有效解。

We considered a nonsmooth multiobjective optimization problem with inequality constraints and set constraint. We first introduced the generalized Abadie constraint qualification and generalized Kuhn-Tucker constraint qualification in terms of Clarke directional derivative,tangent cone,the cone of attainable directions and linearized cone. Furthermore,we proved that Geoffrion proper efficient is generalized Kuhn-Tucker properly efficient under generalized Abadie constraint qualification holds or generalized Kuhn-Tucker constraint qualification holds.