Here is the listing of Best reference books on Advanced Topics in Discrete Optimization.
|1. “Geometric Algorithms and Combinatorial Optimization” by M. Gr ̈tschel, L. Lov ́sz, and A. Schrijver
Book Review: This book demonstrates the theory of linear and integer programming and also demonstrates the algorithms thereby focusing on the complexity analysis. The book also covers recent developments in the field of linear and integer programming. This book is suitable for graduate students and researchers in the field of operations research, mathematics and computer science. The book contains chapters on linear algebra and its complexity, lattice theory and Diophantine equations and their algorithms, polyhedral structure, polarity, blocking and many more.
|2. “Theory of Linear and Integer Programming” by A. Schrijver|
|3. “Geometry of Numbers” by C. Lekkerkerker and P. Gruber
Book Review: This book includes the geometry of numbers along with the relations to other branches of mathematics like analytic number theory, Diophantine approximation, coding and numerical analysis. The book also deals with the convex and non-convex bodies and lattices that are present in Euclidean space. The book also contains newer chapters on the recent developments made in the field of geometry of numbers. The book also demonstrates the progress made in the areas of geometry of numbers and the expected results.
|4. “Optimization Over Integers” by D. Bertsimas and R. Weismantel
Book Review: This book provides a unified treatment in the field of theory of integer optimization. The book is divided into four parts and they are formulations and relaxations, algebra and geometry of integer optimization, integer optimization algorithms and extensions of integer optimizations. The book illustrates the development of integer optimization theory via integral generating sets. The book also focuses on strong formulations, duality and relaxations. The book also discusses applications of lattices and algebraic geometry to integer optimization. The book also covers many enumerative and heuristic methods along with large number of examples and exercises.
|5. ” Algebraic and Geometric Ideas in the Theory of Discrete Optimization” by J. De Loera, R. Hemmecke, and M. K ̈ppe
Book Review: The book covers all the latest advancements in the field of mathematical theory of discrete optimization especially the methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions and many other optimization tools. The book also provides many research technologies and offers many techniques for learning these methods and also provides a transition from linear discrete optimization to nonlinear discrete optimization. The book is suitable for advanced graduate students in the field of mathematics, computer science and operations research.
Sanfoundry Global Education & Learning Series – Best Reference Books!