# mdp_LP: Solves discounted MDP using linear programming algorithm In MDPtoolbox: Markov Decision Processes Toolbox

## Description

Solves discounted MDP with linear programming

## Usage

 `1` ```mdp_LP(P, R, discount) ```

## Arguments

 `P` transition probability array. P is a 3 dimensions array [S,S,A]. Sparse matrix are not supported. `R` reward array. R can be a 3 dimensions array [S,S,A] or a list [[A]], each element containing a sparse matrix [S,S] or a 2 dimensional matrix [S,A] possibly sparse. `discount` discount factor. discount is a real which belongs to ]0; 1[

## Details

mdp_LP applies linear programming to solve discounted MDP for non-sparse matrix only.

## Value

 `V` optimal value fonction. V is a S length vector `policy ` optimal policy. policy is a S length vector. Each element is an integer corresponding to an action which maximizes the value function `cpu_time` CPU time used to run the program

## Examples

 ```1 2 3 4 5 6``` ```# Only with a non-sparse matrix P <- array(0, c(2,2,2)) P[,,1] <- matrix(c(0.5, 0.5, 0.8, 0.2), 2, 2, byrow=TRUE) P[,,2] <- matrix(c(0, 1, 0.1, 0.9), 2, 2, byrow=TRUE) R <- matrix(c(5, 10, -1, 2), 2, 2, byrow=TRUE) mdp_LP(P, R, 0.9) ```

### Example output

```Loading required package: Matrix