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Reformulating Bilevel Problems by SQP Embedding
Author(s) -
Schäfer Kai,
Fliege Jörg,
Flaßkamp Kathrin,
Büskens Christof
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000302
Subject(s) - bilevel optimization , sequential quadratic programming , mathematical optimization , hessian matrix , embedding , mathematics , optimization problem , trust region , computer science , quadratic equation , quadratic programming , process (computing) , artificial intelligence , geometry , computer security , radius , operating system
Due to their inherently complex structure, bilevel optimization problems are often transformed into single‐level problems in order to make them numerically solvable. In this work, we present a novel reformulation strategy, in which we introduce sets of variables and constraints that represent the process of numerically solving the lower‐level problem based on a full step exact Hessian sequential quadratic programming method. The reformulated problem approximates a solution to the original one in the following sense: For a suitable number of imitated lower‐level iteration steps, the lower‐level problem is approximately solved in case a feasible point is found. The approach is illustrated by an example.