Linear Programming: Extreme Points

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Linear Algebra: Efficiency and Complexity

Explores constraints, efficiency, and complexity in linear algebra, emphasizing convexity and worst-case complexity in algorithm analysis.

Linear Programming Basics

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

Hedging for LPs

Covers the concept of hedging for Linear Programs and the simplex method, focusing on minimizing costs and finding optimal solutions.

Branch and Bound: Heuristic Maximization

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

Relations Between Events

Explores relations between events, disjunctive constraints, and modeling with binary variables in optimization problems.

Optimisation in Energy Systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Two-phase Simplex Algorithm: Introduction and Duality

Introduces the two-phase simplex algorithm and explores duality in linear programming.

Simplex Algorithm: Basics

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

Simplex Algorithm: Exercises & Interpretation

Covers exercises on the Simplex Algorithm, optimizing solutions subject to linear constraints.

Certificates: Existence and Proving

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