09-23-2026, 07:55 PM
A First Course in Linear Optimization by Amir Beck and Nili Guttmann-Beck is a 2025 SIAM textbook that develops the foundations of linear optimization from both theoretical and algorithmic perspectives. Starting with linear programming formulations and basic feasible solutions, it introduces the simplex method, duality, and sensitivity analysis, showing how mathematical theory translates into practical optimization procedures. The book also connects linear programming with applications including resource allocation, line fitting, graph coloring, network flows, the traveling salesman problem, and game theory. It is designed as a first undergraduate course and assumes only a first course in linear algebra.
The second half expands from continuous linear programming to discrete and combinatorial optimization. It introduces integer programming, total unimodularity, Gomory cutting planes, and branch-and-bound, explaining why many integer problems are computationally difficult and how practical algorithms nevertheless solve important instances.
Later chapters cover the maximum-flow problem, dynamic programming, and approximation algorithms, giving the reader a broader view of how optimization problems can be attacked when exact solutions are difficult. With 13 chapters and more than 180 exercises, the book aims to combine rigorous mathematical explanations with algorithms and applications rather than treating linear optimization purely as an abstract theory.
BOOK
The second half expands from continuous linear programming to discrete and combinatorial optimization. It introduces integer programming, total unimodularity, Gomory cutting planes, and branch-and-bound, explaining why many integer problems are computationally difficult and how practical algorithms nevertheless solve important instances.
Later chapters cover the maximum-flow problem, dynamic programming, and approximation algorithms, giving the reader a broader view of how optimization problems can be attacked when exact solutions are difficult. With 13 chapters and more than 180 exercises, the book aims to combine rigorous mathematical explanations with algorithms and applications rather than treating linear optimization purely as an abstract theory.
BOOK
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