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's parametric optimization. This book focuses on scenarios with non-unique lower level solutions, exploring both optimistic and pessimistic approaches. It begins with foundational concepts in parametric nonlinear optimization and progresses to key theoretical results, including optimality conditions and solution algorithms. The text also examines stationarity conditions, stability properties, numerical complexity, and integrality constraints, providing a comprehensive overview of bilevel programming challenges.