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Descent approaches for quadratic bilevel programming. (English) Zbl 0819.90076
Summary: The bilevel programming problem involves two optimization problems where the data of the first one is implicitly determined by the solution of the second. We introduce two descent methods for a special instance of bilevel programs where the inner problem is strictly convex quadratic. The first algorithm is based on pivot steps and may not guarantee local optimality. A modified steepest descent algorithm is presented to overcome this drawback. New rules for computing exact stepsizes are introduced and a hybrid approach that combines both strategies is discussed. It is proved that checking local optimality in bilevel programming is an NP-hard problem.

90C26Nonconvex programming, global optimization
90C20Quadratic programming
90C60Abstract computational complexity for mathematical programming problems
Full Text: DOI
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