`convexjlr`

is an `R`

package for Disciplined Convex Programming (DCP) by providing a high level wrapper for Julia package 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`

.

`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`

supports multiple ways to connect to `julia`

, one way is through package `XRJulia`

and the other way is to use package `JuliaCall`

. The differences are as follows:

`XRJulia`

connects to`julia`

, which is the default way for`convexjlr`

, the advantage is the simplicity of the installation process, once you have a working R and working`julia`

, it should be okay to use`convexjlr`

in this way.`JuliaCall`

embeds`julia`

in R, the advantage is the performance, for example, if your convex problem involves large matrice or long vectors, you may wish to use`JuliaCall`

backend for`convexjlr`

; the disadvantage is the installation process, since embedding`julia`

needs compilations, on some types of machines the installation process may be more complicated than`XRJulia`

.

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`

, donâ€™t hesitate to contact me: cxl508@psu.edu.

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:

```
library(convexjlr)
#>
#> Attaching package: 'convexjlr'
#> The following object is masked from 'package:base':
#>
#> norm
## If you wish to use JuliaCall backend for performance
convex_setup(backend = "JuliaCall")
#> Doing initialization. It may take some time. Please wait.
#> Julia version 0.6.2 at location /Applications/Julia-0.6.app/Contents/Resources/julia/bin will be used.
#> Julia initiation...
#> Finish Julia initiation.
#> Loading setup script for JuliaCall...
#> Finish loading setup script for JuliaCall.
#> [1] TRUE
```

And this is our linear regression function using `convexjlr`

:

```
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.

```
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
#> [,1]
#> [1,] 5.003240727
#> [2,] 0.991592939
#> [3,] -0.013119040
#> [4,] 2.008251896
#> [5,] 0.004306522
```

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