Bilevel Optimization: Advances and Next Challenges

A field-defining survey of hierarchical optimization

Bilevel Optimization: Advances and Next Challenges brings together expert surveys on one of mathematical optimization’s most distinctive problem classes: models with a leader-follower structure, where one decision is made in anticipation of another. Edited by Stephan Dempe and Alain Zemkoho, the volume gives readers a broad and carefully organized view of the subject’s evolution, from foundational game-theoretic ideas to current research questions.

What makes this collection especially useful is its scope. Rather than concentrating on a single algorithm or narrow subtopic, it maps the field across theory, methods, applications, and research tools. The result is a volume that works both as an entry point for newcomers and as a reference for readers who want to understand how bilevel optimization is being studied today.

What the volume covers

• Game theory and applications, including Stackelberg-style models and related solution concepts.
• Theory and methods for linear, nonlinear, smooth, and nonsmooth bilevel problems.
• Extensions and uncertainty, including multiobjective models, optimal control, and stochastic formulations.
• Numerical and research tools, including a curated example library and a large bibliography.

Why it stands out

This is an edited survey volume, so the emphasis is on breadth, perspective, and research orientation. The chapters are designed to show where the field has developed, what methods are currently used, and which problems remain difficult. That makes the book particularly valuable for readers working in optimization, operations research, economics, machine learning, and related areas where hierarchical decision models appear naturally.

For readers who want the bigger picture

If you need a current map of bilevel optimization rather than a single-method manual, this title offers a strong one. It is especially well suited to graduate-level study, research planning, and anyone building a working understanding of this technically demanding area.