**Combinatorial Optimization Notes PDF**

*Date: 31st Jan 2023*

In these “** Combinatorial Optimization Notes PDF**”, we will study the fundamentals of combinatorial optimization to the students in terms of both theory and applications, so as to equip them to explore the more advanced areas of convex and non-convex optimizations.

We have provided multiple complete Combinatorial Optimization Lecture Notes PDF for any university student of BCA, MCA, B.Sc, B.Tech CSE, M.Tech branch to enhance more knowledge about the subject and to score better marks in the exam. Students can easily make use of all these Combinatorial Optimization Lecture Notes PDF by downloading them.

**Topics in our Combinatorial Optimization Notes PDF**

The topics we will cover in these **Combinatorial Optimization Notes PDF** will be taken from the following list:

**Introduction to Combinatorial Optimization Problems, Linear and Integer Programs:** LP Formulation, understanding integer programs, computational complexities of IP vs LP, using LP to find optimal or approximate integral solutions, concept of integrality gap.

**Theory of Linear Programming and Algorithmic Perspective to Simplex Method: **standard vs equational form, basic feasible solutions, convexity and convex polyhedra, correspondence between vertices and basic feasible solutions, geometry of Simplex algorithm, exception handling (unboundedness, degeneracy, infeasibility), Simplex algorithm, avoiding cycles.

**Primal-Dual Algorithms: **interpretation of dual, optimality conditions for primal and dual, weak and strong duality, complementary slackness, primal-dual algorithm for the shortest path problem.

**Network Flows: **linear programming formulations for network flows and bipartite matching, totally unimodular matrices integral polyhedral.

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