New optimality conditions and a scalarization approach for a nonconvex semi-vectorial bilevel optimization problem. (English) Zbl 1476.90297
The author transforms a bilevel optimization problem into a scalar-objective optimization problem and proves some theoretical properties. In a bilevel optimization problem the feasible region of the upper level optimization problem is limited to the solution set of the lower level optimization problem. Necessary local optimality conditions are introduced. A new scalarization technique, different to the classical scalarization approach is provided for nonconvex semivectorial optimization problems. A transformation to a single level optimization problem is provided and KKT-type necessary optimality conditions are derived. The method is applicable to nonconvex optimization problems.
Reviewer: Erwin Pesch (Siegen)
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C26 | Nonconvex programming, global optimization |
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
| 49K99 | Optimality conditions |
Keywords:
semivectorial bilevel optimization; weakly efficient solution; optimal value function; optimality conditions; multiobjective optimizationReferences:
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