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README.Rmd
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README.Rmd
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---
output: rmarkdown::github_document
---
<!-- README.md is generated from README.Rmd. Please edit that file -->
# Convex Optimization in R by convexjlr
[](https://travis-ci.org/Non-Contradiction/convexjlr)
[](https://ci.appveyor.com/project/Non-Contradiction/convexjlr)
[](https://cran.r-project.org/package=convexjlr)
[](https://cran.r-project.org/package=convexjlr)
[](https://cran.r-project.org/package=convexjlr)
```{r, echo = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "README-"
)
## set seed for reproducible result
set.seed(123)
```
`convexjlr` is an `R` package for *Disciplined Convex Programming (DCP)* by providing
a high level wrapper for Julia package [Convex.jl](https://github.com/JuliaOpt/Convex.jl).
The aim is to provide optimization results rapidly and reliably in `R`
once you formulate your problem as a convex problem.
`convexjlr` can solve linear programs, second order cone programs, semidefinite programs, exponential cone programs, mixed-integer linear programs, and some other DCP-compliant convex programs through `Convex.jl`.
## Installation
`convexjlr` is on CRAN now! To use package `convexjlr`, you first have to install Julia
<https://julialang.org/> on your computer, and then you can install `convexjlr` just like
any other R packages.
Note: `convexjlr` used to support multiple ways to connect to `julia`, one way was through package `XRJulia` and the other way was to use package `JuliaCall`. The latter approach was more performant and thus the default approach.
But due to the fact that `XRJulia` doesn't support `julia` v0.7 and v1.0 yet, only `JuliaCall` backend is supported currently.
We hope you use `convexjlr` to solve your own problems.
If you would like to share your experience on using `convexjlr` or have any questions about `convexjlr`,
don't hesitate to contact me: <cxl508@psu.edu>.
## Quick Example
We will show a short example for `convexjlr` in solving linear regression problem.
To use package `convexjlr`, we first need to attach it and do the initial setup:
```{r}
library(convexjlr)
## If you wish to use JuliaCall backend for performance
convex_setup(backend = "JuliaCall")
```
And this is our linear regression function using `convexjlr`:
```{r}
linear_regression <- function(x, y){
p <- ncol(x)
## n is a scalar, you don't have to use J(.) to send it to Julia.
n <- nrow(x) ## n <- J(nrow(x))
## x is a matrix and y is a vector, you have to use J(.) to send them to Julia.
x <- J(x)
y <- J(y)
## coefficient vector beta and intercept b.
beta <- Variable(p)
b <- Variable()
## MSE is mean square error.
MSE <- Expr(sumsquares(y - x %*% beta - b) / n)
## In linear regression, we want to minimize MSE.
p1 <- minimize(MSE)
cvx_optim(p1)
list(coef = value(beta), intercept = value(b))
}
```
In the function, `x` is the predictor matrix, `y` is the response we have.
And the `linear_regression` function will return the coefficient and intercept solved by `cvx_optim`.
Now we can see a little example using the `linear_regression` function we have just built.
```{r}
n <- 1000
p <- 5
## Sigma, the covariance matrix of x, is of AR-1 strcture.
Sigma <- outer(1:p, 1:p, function(i, j) 0.5 ^ abs(i - j))
x <- matrix(rnorm(n * p), n, p) %*% chol(Sigma)
## The real coefficient is all zero except the first, second and fourth elements.
beta0 <- c(5, 1, 0, 2, 0)
y <- x %*% beta0 + 0.2 * rnorm(n)
linear_regression(x, y)$coef
```
## More Examples
More examples (including using `convexjlr` for Lasso, logistic regression and Support Vector Machine) can be found in the pakage vignette or on the github page: <https://github.com/Non-Contradiction/convexjlr>