Simplex Method: Phase 2

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Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Linear Systems: Chapters 4, 5, 6

Explores the link between linear systems and optimization through elimination and LU decomposition.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Optimisation with Constraints: Interior Point Algorithm

Explores optimization with constraints using KKT conditions and interior point algorithm on two examples of quadratic programming.

ALM with Inequalities: Next Steps in Optimization

Explores the Augmented Lagrangian Method with equality and inequality constraints in optimization, emphasizing the importance of slack variables.

Linear Optimization: Finding Initial BFS

Explains the process of finding an initial Basic Feasible Solution for linear optimization problems using the Simplex Algorithm.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Solving Linear Programs: SIMPLEX Method

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

Hedging for LPs

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