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MATH-261: Discrete optimization

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Lectures in this course (65)

Shortest Path Problems: Bellman-Ford Log in to Mediaspace to watch this video

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

Bellman-Ford Algorithm: Shortest Path Log in to Mediaspace to watch this video

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

Shortest Path: Introduction Log in to Mediaspace to watch this video

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

Bellman Ford Algorithm Log in to Mediaspace to watch this video

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

Linear Programming Duality Log in to Mediaspace to watch this video

Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.

Introduction to Shortest Path Log in to Mediaspace to watch this video

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

Dijkstra's Algorithm and Shortest Path Log in to Mediaspace to watch this video

Covers Dijkstra's algorithm for shortest path problems and its application in ALL-TO-ONE and ALL-PAIRS algorithms.

Dynamic Programming: Bellman-Ford and Dijkstra Log in to Mediaspace to watch this video

Explores dynamic programming with Bellman-Ford, Dijkstra, greedy strategies, and activity scheduling problems.

Dynamic Programming: How Many Ways to Make Change Log in to Mediaspace to watch this video

Demonstrates dynamic programming to find the number of ways to make change using different coin denominations.

Discussion of Complexity Log in to Mediaspace to watch this video

Explores worst-case complexity in computer science and the importance of real-life complexity in algorithm selection.

Greedy Strategy and Dynamic Programming Log in to Mediaspace to watch this video

Explores the concepts of greedy strategy and dynamic programming in building optimal solutions for various problems.

Network Flows and LP Formulations Log in to Mediaspace to watch this video

Explains network flows, LP formulations, simplex method, duality, and practical applications.

Review Sessions and Exam Preparation Log in to Mediaspace to watch this video

Discusses review sessions, exam preparation, problem-solving focus, and collaborative exam planning.

Linear Programming Basics Log in to Mediaspace to watch this video

Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.

Simplex Method: Basics and Applications Log in to Mediaspace to watch this video

Covers the basics of the Simplex method and its application in solving optimization problems.

LP Duality: An Economics Perspective Log in to Mediaspace to watch this video

Explores LP duality in zero-sum games from an economics perspective, emphasizing optimal strategies and decision-making.

Duality in Linear Programming Log in to Mediaspace to watch this video

Explores the concept of duality in linear programming, discussing the relationship between primal and dual problems.

Integer Programming and Network Flows Log in to Mediaspace to watch this video

Covers the fundamentals of integer programming and network flows in directed graphs.

Network Flow Algorithms Log in to Mediaspace to watch this video

Covers network flow algorithms, including Max Flow, Min Cut, and Negative Cost Cycle Algorithm, progressing from basic definitions to advanced algorithms like Bellman-Ford and Dijkstra's.

Dual Translations in Linear Programming Log in to Mediaspace to watch this video

Explores dual translations in linear programming, emphasizing primal and dual formulations and the significance of invertible submatrices.

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