Foundations of Bilevel Programming

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Bilevel programming problems involve hierarchical optimization, where the upper level's constraints depend on a lower level optimization problem. This book focuses on scenarios with non-unique lower level solutions, examining both optimistic and pessimistic approaches. It begins with essential concepts in parametric nonlinear optimization, then presents key theoretical results, including optimality conditions and solution algorithms. The text also explores transforming optimistic bilevel problems into single-level ones, discussing stability, numerical complexity, and integrality conditions.