Integer Programming: Doignon's Theorem

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

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Solving Integer Linear Programs

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Convex Hulls: Complexity and Vertices

Explores the complexity of convex hulls and the concept of vertices within them.

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Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

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Optimization with Constraints: KKT Conditions

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Linear Programming: Weighted Bipartite Matching

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