Two-phase Simplex Algorithm: Introduction and Duality

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Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Duality in Linear Programming

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

Linear Optimization Techniques: Problem Solving Approaches

Provides an overview of linear optimization techniques, focusing on problem-solving methods and the importance of constraints and objective functions.

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.

Dual Translations in Linear Programming

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

Discrete Optimization: Relaxation

Explores solving discrete optimization problems by relaxing integrality constraints.

Linear Optimization: Fundamentals

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.

Branch & Bound: Optimization

Covers the Branch & Bound algorithm for efficient exploration of feasible solutions and discusses LP relaxation, portfolio optimization, Nonlinear Programming, and various optimization problems.