Combinatorial Optimization

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Combinatorial Optimization. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Polyhedra; Linear programs; Duality; Integrality. Shortest paths; Minimum spanning trees; Cut properties; Exchange arguments. Maximum flow; Minimum cuts; Flow decomposition; Min-cost flow. Bipartite matching; General matching; Assignment problems; Matching polytopes. Matroids; Independence systems; Greedy optimality; Matroid intersection. Integer programming; Branch and bound; Cutting planes; Relaxations. Approximation ratios; Primal-dual methods; Randomized rounding; Local search. Submodular optimization; Facility location; Scheduling; Optimization project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.