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On the solution of convex bilevel optimization problems. (English) Zbl 1343.90065
Summary: An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the Fritz-John necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the Karush-Kuhn-Tucker conditions.

MSC:
90C26 Nonconvex programming, global optimization
91A65 Hierarchical games (including Stackelberg games)
Software:
Optknock
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