Lectures related to Integer Programming: Doignon's Theorem

Linear Programming Basics

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

Linear Programming: Convex Hull

Covers MAE regression, convex hull, reformulation advantages, and practical problems with decision variables and constraints.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Solving Integer Linear Programs

Covers solving integer linear programs graphically, algorithmically, and through optimization methods.

Convex Hulls: Complexity and Vertices

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

Optimal Transport: Rockafellar Theorem

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

Optimal Decision Making: Integer Programming

Covers integer programming, convex hulls, Gomory cutting planes, and branch and bound methods.

Optimization with Constraints: KKT Conditions

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

Linear Programming: Weighted Bipartite Matching

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

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Linear Programming Techniques in Reinforcement Learning

Covers the linear programming approach to reinforcement learning, focusing on its applications and advantages in solving Markov decision processes.

Linear and Integer Programming

Covers the theory of linear and integer programming, focusing on the integer hull and rational polyhedra.

Optimisation Problem: Solving by FM

Covers the modelling and optimization of energy systems, focusing on solving optimization problems with constraints and variables.

Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.

Integer Programming: John's Theorem

Explores integer programming, John's Theorem, and the reduction to shortest vector computations in convex bodies.

Convex Optimization: Gradient Descent

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

KKT Conditions: Convex Optimization

Explores the KKT conditions in convex optimization, including dual cones, SDP duality, and convex hulls.

KKT and Convex Optimization

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.