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| Volume 2, Number 3, September 2006, pp.447-467 | |||||||||
| Henri Bonnel | |||||||||
| Key words: | |||||||||
| bilevel optimization, multiobjective optimization, parameterized linear programming, optimization over the efficient set | |||||||||
| Mathematices Subject Classification: 90C29, 90C30, 90C48, 90C31, 90C05. | |||||||||
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| Abstract: | ||||
| The paper studies a bilevel optimization problem with a lower level given by a convex vector minimization problem. In this case the lower level usually has multiple solutions, thus the so called optimistic formulation is considered. Necessary optimality conditions are obtained when dealing with properly efficient solutions as well as weakly efficient solutions for the lower level. An application to the case when the lower level is given by a linear multiobjective optimization problem (with data having a C 1-dependence on parameters) is given. | ||||
| Optimality conditions for the semivectorial bilevel optimization problem | ||