Analysis, probability, statistics and PDE
engineering student course, CentraleSupélec, MICS, 2018
This course is served as an reinfocing course to programs in mathematics
Analysis Probability and PDE
Slack
The communication is available on whatsapp and Wechet
Lectures
| Entry | Description | |
|---|---|---|
| 01 | Introduction | Introduction to optimisation |
| 02 | The Simplex algorithm | An algorithm for solving linear programs |
| 03 | Limit cases of the Simplex | The limiting cases for the simplex, like how to start it |
| 04 | Duality | LP and duality. Interpretation and algorithms |
| 05 | Integer Programming | Formulation and examples |
| 06 | IP resolution | Resolution of Integer Programs: Cuts and Branch & Bound |
| 07 | Transport Problems | Transport problems are a simpler case of LP/IP |
| 08 | Resolution of transport problems | Resolution of transport problems |
| 09 | Network problems | Network problems, including maxflow and the network simplex |
Tutorials
| Entry | Description | |
|---|---|---|
| 01 | Tutorial 1 text | Simplex algorithm, examples, formulations |
| 02 | Tutorial 2 text | Solving LP problems with spreadsheets. Duality |
| 03 | Tutorial 3 text | This tutorial is on integer programming |
| 04 | Tutorial 4 text | This tutorial is assignment 1 |
| 05 | solving the TSP | Solving the TSP. This is assignment 2 |
Reinforcement courses
| Entry | Description | |
|---|---|---|
| 16 | MR16 statistique | solution included |
| 05 | solving the TSP | Solving the TSP. This is assignment 2 |
Solutions and code
| Entry | Description | |
|---|---|---|
| 01 | Tutorial 1 solution | Solution to the first tutorial |
| 02 | a Python Simplex solver | Basic, commented Simplex solver |
| 03 | Sudoku solver | This code requires cvxopt. |
Code 1
Here you will find verbose, straightforward, numpy-based code for the simplex.
Here is the basic code, a Python Simplex solver, with no claim with respect to efficiency. Here is a Python Notebook, with worked out examples.
I recommend you try the Python Notebook version. Here is the online rendering of this notebook.
Thanks
Special thank to Dr.Brice Hannebicque
Sudoku solver
Here is a nice Sudoku solver written in Python. It requires cvxopt.
Challenges
good luck for the finak
Other relevant challenges will be posted here.
Alternative project
The Kaggle challenge is obviously very challenging. An alternative project is to implement a peg-solitaire solver.
Here are a couple of articles on how this might be done Article 1 ; Article 2.