Course

MATH-261: Discrete optimization

Lectures in this course (65)

Explores network flows, simplex method, linear programming, tree solutions, and dual solutions in optimization problems.

Explores convex polyhedra, linear programs, and their optimization importance.

Covers the basics of integer programming, focusing on problems with integer values and discussing the simplex algorithm.

Covers linear inequalities, active constraints, and equivalent linear programs.

Revisits network flows with capacities, focusing on bounded flow problems and different formulations to approach them.

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Covers the basics of linear programming and the simplex method, focusing on finding optimal solutions and handling degeneracy.

Explores the Ford-Fulkerson algorithm for solving the Max-Flow problem and its applications in network flow optimization.

Covers solving bounded network flow problems by adjusting flow capacities and constraints, including binary programs.

Explores certificates, proving solution existence, constraints, and linear programming duality.

Explores duality theorems in linear programming, emphasizing optimal solutions and degeneracies.

Demonstrates the Ford-Fulkerson algorithm through a step-by-step worked example.

Explores solving shortest path problems with the Bellman-Ford algorithm and negative cost cycles.

Explores the Forkas Lemma and the Theorem of the Alternatives in linear equation systems.

Explores separating hyperplanes for two sets X and Y, discussing conditions for separation and implications of convexity.

Provides an example of the Bellman-Ford algorithm for finding the shortest path in a graph.

Explores zero-sum games and the minimax theorem in Game Theory, emphasizing optimal strategies.

Covers one-to-one shortest path, negative cost edges, and optimal solutions.

Explores the Bellman Ford algorithm for finding the shortest path in graphs with negative edge weights.

Introduces the basics of integer programming, including binary integer programs and constraint strategies.