Python scripts to solve optimization problems step by step, covering linear, integer, network, and non-linear programming.
Linear Programming (LP):
- Compute the initial basis for the simplex algorithm given a specific point
- Simplex algorithm, optimal solution
- Gomory cuts to find integer solutions
Network Linear Programming:
- Compute flow and potential given a T, L, U partition
- Simplex algorithm applied to capacitated networks
- Dijkstra (shortest path tree)
- Max-Flow / Min-Cut: find max flow and the corresponding min-cut
Integer Linear Programming (ILP):
- Knapsack problem
- Traveling Salesman Problem (TSP)
- Branch & Bound
Non-Linear Programming (NLP):
- Stationary points categorization
- Projected gradient method
- Karush-Kuhn-Tucker conditions (KKT)