On an algorithm solving two-level programming problems with nonunique lower level solutions

On an algorithm solving two-level programming problems with nonunique lower level solutions

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Article ID: iaor19981345
Country: Netherlands
Volume: 6
Issue: 3
Start Page Number: 227
End Page Number: 249
Publication Date: Nov 1996
Journal: Computational Optimization and Applications
Authors: ,
Abstract:

In the paper, an algorithm is presented for solving two-level programming problems. This algorithm combines a direction finding problem with a regularization of the lower level problem. The upper level objective function is included in the regularization to yield uniqueness of the follower's solution set. This is possible if the problem functions are convex and the upper level objective function has a positive definite Hessian. The computation of a direction of descent and of the step size is discussed in more detail. Afterwords the convergence proof is given. Last but not least some remarks and examples describing the difficulty of the inclusion of upper level constraints also depending on the variables of the lower level are added.

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