Linear Programming 2: Theory and Extensions - Advanced Theory

In this review of Linear Programming 2: Theory and Extensions the reviewer finds a rigorous, theory-forward continuation for readers already familiar with core linear programming concepts. This volume is best for graduate students, researchers, and practitioners who need deeper explanations of algorithms beyond basic treatments; the single biggest reason to buy is its thorough coverage of advanced methods such as variants of the simplex, early and modern interior point techniques, and decomposition approaches that are rarely collected together in one place. The tone is scholarly and assumes comfort with formal proofs and prior exposure to linear programming.

Key Features

• Advanced algorithm coverage: Presents variants of the simplex method and modern interior point methods so readers can compare practical and theoretical tradeoffs.
• Theory extension: Expands on foundational material to develop formal proofs and convergence results useful for researchers and instructors.
• Decomposition and GUB: Includes decomposition techniques and generalized upper bound formulations that help tackle large structured problems.
• Integer programming link: Explores relationships to integer programming, offering a bridge from continuous to discrete optimization topics.
• Game theory connections: Discusses game theoretic formulations that illuminate duality and strategic models within linear programming.

Who It's For

Graduate students in operations research or applied mathematics who have completed an introductory linear programming course will get the most from this book, as will academics and advanced practitioners seeking a compact reference on advanced methods. Instructors designing a second-semester course on linear programming theory will find numerous topics to structure lectures and proofs around.

Those who should look elsewhere include beginners without prior exposure to the simplex algorithm or readers seeking a computational how-to focused on software and implementation details; the emphasis here is on theory and method rather than step-by-step coding or commercial solver guidance.

Pros & Cons

Pros

• Comprehensive treatment of advanced methods gives a coherent picture of variants of the simplex and interior point approaches.
• Strong theoretical development supports use as a graduate-level reference for proofs and method analysis.
• Inclusion of decomposition, GUB, integer programming, and game theory provides useful cross-topic connections.

Cons

• The book assumes significant prior knowledge, so it is not well suited to novices seeking an introductory or implementation-focused text.

Specifications

Title	Linear Programming 2: Theory and Extensions
Series	Springer Series in Operations Research and Financial Engineering
Authors	George B. B. Dantzig, Mukund N. Thapa
Focus areas	Simplex variants, interior point methods, decomposition, GUB, integer programming, game theory
Intended audience	Graduate students, researchers, advanced practitioners
Approach	Theoretical development with formal proofs and method analysis

Our Verdict

Linear Programming 2 is an excellent theoretical follow-up for readers who need deeper understanding of advanced linear programming methods; its breadth across simplex variants, interior point approaches, decomposition, and related topics makes it good value as a graduate reference. Purchase it if you want rigorous proofs and method comparisons rather than introductory tutorials or implementation guides.

Frequently Asked Questions

Is this book suitable for beginners?
No. The book assumes prior knowledge of basic linear programming, including the simplex algorithm, and is written for more advanced study.

Does it cover computational implementations?
Not primarily; the emphasis is on theory and algorithmic variants rather than solver code or practical software tutorials.

Will it help with integer programming?
Yes. The text includes material connecting linear programming techniques to integer programming formulations and methods.