MATH-261: Discrete optimization

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Lectures in this course (65)

Dijkstra's Algorithm Overview Log in to Mediaspace to watch this video

Demonstrates the iterative process of applying Dijkstra's algorithm to find optimal paths.

Linear Programming Duality Log in to Mediaspace to watch this video

Explores the concept of duality in linear programming and its practical implications in optimization.

Convex Polyhedra and Linear Programs Log in to Mediaspace to watch this video

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

Linear Inequalities and Equivalent LP Log in to Mediaspace to watch this video

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

Solving Linear Programs: SIMPLEX Method Log in to Mediaspace to watch this video

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

Linear Programming Basics Log in to Mediaspace to watch this video

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

Certificates: Existence and Proving Log in to Mediaspace to watch this video

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

Duality Theorems Log in to Mediaspace to watch this video

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

Forkas Lemma: Theorem of the Alternatives Log in to Mediaspace to watch this video

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

Separating Hyperplanes: Theory and Applications Log in to Mediaspace to watch this video

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

Game Theory: Minimax Theorem Log in to Mediaspace to watch this video

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

Integer Programming Basics Log in to Mediaspace to watch this video

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

Linear Programming Basics Log in to Mediaspace to watch this video

Explores linear programming basics, including basic solutions, feasible solutions, optimal solutions, and challenges in solving integer programming problems.

Integer Program Formulation Log in to Mediaspace to watch this video

Covers the process of formulating integer programs and improving solutions.

Branch and Bound: Heuristic Maximization Log in to Mediaspace to watch this video

Explains the Branch and Bound algorithm for heuristic maximization problems using LP relaxations and pruning techniques.

Introduction to Graph Theory Log in to Mediaspace to watch this video

Covers the basics of graph theory, including network flows, degrees of vertices, walks, and subgraphs.

Graph Theory and Network Flows Log in to Mediaspace to watch this video

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Graph Theory Basics Log in to Mediaspace to watch this video

Introduces induced flows, basis matrices, and tree solutions in graph theory.

Simplex Algorithm: Basics Log in to Mediaspace to watch this video

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

Max Flow Problem Log in to Mediaspace to watch this video

Covers the max flow problem, weak duality, and the Ford-Fulkerson algorithm.

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