Exact methods: Gomory cuts

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Covers the main idea behind the Simplex algorithm and explains the Tableau method for solving linear programming problems.

Linear Programming: Two-phase Simplex Algorithm

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Optimal Decision Making: Integer Programming

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

Linear Programming: Solving LPs

Covers the process of solving Linear Programs (LPs) using the simplex method.

Linear Programming Basics

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

Simplex Algorithm: Basics

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

Optimisation Problem: Solving by FM

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

Integer Programming Basics

Introduces the basics of integer programming, including binary integer programs and constraint strategies.

Iterative Rounding Heuristic

Explores optimal integer programming, Gomory cuts, and an iterative rounding heuristic.

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.