Theory of Linear and Integer Programming

Theory of Linear and Integer Programming presents a comprehensive mathematical treatment of optimization theory, focusing on linear programming and its extension to integer programming. The text covers fundamental concepts including duality theory, the simplex method, cutting plane techniques, and polyhedral theory. The book progresses systematically from basic linear algebra foundations through advanced topics in computational complexity and algorithmic approaches. Schrijver includes detailed proofs and extensive technical appendices that support the main theoretical developments. Beyond the core material, the work explores connections to combinatorial optimization and examines applications in areas like network flows and matching theory. The presentation balances abstract theory with concrete examples and computational methods. This text stands as an authoritative reference that bridges pure mathematics and practical computation in optimization theory. Its rigorous treatment highlights the deep relationships between linear programming, discrete mathematics, and computer science.

Readers describe this as a mathematically rigorous textbook requiring significant background in linear algebra and optimization. Multiple reviewers note it works better as a reference than a self-study guide. Liked: - Clear, precise proofs and theorems - Comprehensive coverage of both theory and algorithms - Strong focus on computational complexity - High-quality exercises with solutions Disliked: - Dense writing style makes concepts hard to grasp - Requires more prerequisites than other LP books - Limited worked examples - Some sections are too abstract for practical use One reviewer on Amazon states "This is not a book to learn from, but rather to consult once you already understand the material." A Goodreads review notes "The theory is deep but the presentation could be more intuitive." Ratings: Goodreads: 4.14/5 (22 ratings) Amazon: 4.3/5 (12 ratings) Mathematical Association of America: Recommended for graduate-level study

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🔢 Alexander Schrijver is not only a mathematician but also a historian of mathematics, and has made significant contributions to documenting the history of optimization theory. 📚 The book, published in 1986, has become one of the most cited references in linear programming and is used in graduate-level courses worldwide. 🎯 The theory presented in this book has direct applications in manufacturing, transportation logistics, and financial portfolio optimization. 🏅 Schrijver received the Fulkerson Prize in 1982 for his work on path systems and flow algorithms, topics that are foundational to parts of this book. 💡 While most linear programming texts focus on the simplex method, this book gives equal weight to ellipsoid and interior point methods, which proved crucial for later developments in the field.