Convex Optimization in R by convexjlr

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.

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 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. Note that if you have the latest julia version (v0.6.0) installed, then you have to use the latest version of XRJulia on github: devtools::install_github("johnmchambers/XRJulia").

• 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.

And there are several backward incompatible issues in julia v0.6 and julia v0.5 and corresponding version of Convex.jl, so if you are using julia v0.6, please use convexjlr with care.

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:

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 at location /Applications/Julia-0.6.app/Contents/Resources/julia/bin will be used.
#> Julia version 0.6.0 found.
#> 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

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