Linear Programming: Weighted Bipartite Matching

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Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Approximation Algorithms

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

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Optimization Methods: Theory Discussion

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

Linear Programming Basics

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

Optimization with Constraints: KKT Conditions

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

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Relations Between Events

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

Linear Programming Duality

Covers linear programming duality and complementary slackness condition.