Fenchel and Disjunctive Decomposition for Stochastic Mixed-Integer Programming

Erscheinungsjahr 2026
ISBN: 978-3-032-34349-9
Verlag: Springer

Buch, Englisch, 205 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Springer Optimization and Its Applications

This book introduces readers to the innovative world of Fenchel and disjunctive decomposition for tackling stochastic mixed-integer programming (SMIP) problems. SMIP is a crucial area of stochastic programming that addresses optimization challenges under uncertainty with discrete decision variables, applicable in fields like healthcare, transportation, and energy planning.

Key concepts explored include the foundational theories of Fenchel decomposition (FD) and disjunctive decomposition (D²), as well as their integration into FDD. The book provides a comprehensive look at decomposition algorithms and their practical implementation, offering numerical illustrations to guide readers in applying these methods to real-world problems. Chapters delve into topics such as mean-risk SMIP models, risk-neutral and risk-averse settings, and advanced techniques like FDD with integer set reduction (FDD-ISR).

Ideal for students, researchers, and practitioners with a background in mathematical programming, this book offers new insights and algorithms for solving complex SMIP problems. It stands out by emphasizing both theoretical foundations and practical applications, making it an essential resource for anyone interested in advancing their understanding of stochastic programming.

Zielgruppe

Research

Autoren/Hrsg.

Ntaimo, Lewis

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Part I Preliminaries.- 1 Introduction.- 2 The Mean-Risk Stochastic Mixed-Integer Programming Model.- Part II Theoretical Foundations.- 3 Basic Decomposition Algorithm for Mean-Risk Stochastic.- 4 Foundations of Fenchel Decomposition.- 5 Foundations of Disjunctive Decomposition.- Part III Algorithms and Numerical Illustrations.- 6 Fenchel Disjunctive Decomposition: Risk-Neutral Setting.- 7 Fenchel Disjunctive Decomposition with Integer Set Reduction.- 8 Fenchel Disjunctive Decomposition: Mean-Risk Setting.- Appendix A Fenchel Disjunctive Decomposition.