Linear and Integer Programming: Polyhedra and Unimodularity

Combinatorial and integer optimization form the backbone of modern algorithmic problem-solving in computer science and operations research. This course provides a clear, conceptual foundation in linear programming geometry, explaining why and when continuous methods yield exact integer solutions. You will explore fundamental mathematical structures, polyhedral theory, and network algorithms from the ground up. What you'll learn: - Understand basic feasible solutions, extreme points, and the geometry of convex polyhedra - Master total unimodularity and its role in guaranteeing integer solutions - Apply unimodularity criteria to classic problems like bipartite matching and optimal network circulation - Explore separation oracles, ellipsoid methods, and modern cutting-plane concepts - Analyze foundational complexity and algorithmic guarantees in discrete optimization The course begins with fundamental linear algebra definitions and polyhedral terminology before progressing into matrix characterizations, graph-based applications, and algorithmic approaches. Written for students, programmers, and analysts looking to build rigorous optimization fundamentals without prior advanced prerequisites. Begin reading today to strengthen your discrete optimization skills.