## MatrixOptim.jl

Data-Driven Decision Making under Uncertainty in Matrix
Author edxu96
Popularity
14 Stars
Updated Last
1 Year Ago
Started In
April 2019

# MatrixOptim.jl

MILP, Robust Optim. and Stochastic Optim., Decomposition Algorithms, and more in Matrix. `MatrixOptim.jl` is a package to model and solve optimization in uncertain context. The templates for robust optimization and stochastic optimization formulated in matrix are very coherent comprehensive, and the algorithms in matrix are very explicit.

This is a package I developed in 2019. Don't know too much about tests and documentation that time. I am trying to keep it up-to-date these days.

## Introduction

The MILP can always be formulated in the following matrixes:

``````min  vec_c' * vec_x + vec_f' * vec_y
s.t. mat_A * vec_x + mat_B * vec_y <= vec_b
vec_x in R
vec_y in Z
``````

## Installation and Test

``````(v1.1) pkg> add MatrixOptim
``````
``````(v1.1) pkg> test MatrixOptim
``````

## How to Use

For mixed integer linear programming:

```model = getModel(vec_c, mat_aa, vec_b)
solveModel!(model)```

For mixed integer linear programming with Benders decomposition:

```model = getModelBenders(n_x, n_y, vec_min_y, vec_max_y, vec_c, vec_f, vec_b, mat_aa, mat_bb)
solveModelBenders!(model)```

Right now, the supported solver is `GLPK`. Will add the feature to select other solvers, like `Gurobi` and `CPLEX` later.

## Features

### Models

• Linear Programming
• Mixed Integer Linear Programming
• Robust Optimization
• Stochastic Optimization
• Markov Decision Process
• Dynamic Optimization

### Algorithms

• Simplex Method
• Branch and Cut for MILP
• Benders Decomposition for MILP
• L-Shaped Benders Decomp for Stochastic Optim
• Dantzig-Wolfe Decomposition Family