A First Course in Linear Optimization

This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability to apply the theory and algorithms to actual problems. To deepen the reader’s understanding, the authors provide many applications from diverse areas of applied sciences, such as resource allocation, line fitting, graph coloring, the traveling salesman problem, game theory, and network flows. The book also includes more than 180 exercises, most of them with partial answers and about 70 with complete solutions, as well as a continuous illustration of the theory through examples and exercises. A First Course in Linear Optimization is intended to be read cover to cover and requires only a first course in linear algebra as a prerequisite. Its 13 chapters can be used as lecture notes for a first course in linear optimization.

Amir Beck is a professor in the School of Mathematical Sciences at Tel-Aviv University. He has published numerous papers and has given invited lectures at international conferences. He was awarded the INFORMS Farkas Prize (2022), the Salomon Simon Mani award for excellence in teaching, and the Henry Taub research prize. He is a co-editor of Mathematical Programming Series A and was an associate editor of Mathematics of Operations Research, SIAM Journal on Optimization, and Journal of Optimization Theory and Applications, as well as an area editor for optimization in Operations Research. His research interests are in continuous optimization, including theory, algorithmic analysis, and applications.

Nili Guttmann-Beck is a senior lecturer at the Academic College of Tel Aviv-Yaffo, where she heads the statistics education unit. Her research focuses on optimization algorithms and combinatorial algorithms in graphs as well as the pedagogy of statistics.