qpmadr

qpmadr provides R-bindings to the quadratic programming-solver qpmad, written by Alexander Sherikov.

Installation

You can install the released version of qpmadr from CRAN with:

install.packages("qpmadr")

Example

This is an example which shows you how to solve a simple problem:

[ \min_{\rm x}{ \space x'H x} ]

[ s.t. \space \sum_{i}{x_i} = n ]

[ -2 \leq x_i \leq 2 ]

where (H) is a random positive definite matrix of size (n \times n), and (x) is a (column) vector of size (n).

The code below will run a benchmark against the quadprog solver for n=100, checking that both give the same results.

library(qpmadr)
library(quadprog)
library(microbenchmark)


set.seed(42)

n = 100

H = crossprod(matrix(rnorm(n*n), n))

# constraint specification for qpmadr
lb = -2
ub = 2
A = matrix(1, 1, n)
Alb = n
Aub = n

# constraint specification for quadprog
At = cbind(rep_len(1, n), diag(1, n, n), diag(-1, n, n))
b = c(n, rep_len(-2, 2*n))



bm = microbenchmark(
  check    = "equal",
  qpmadr   = qpmadr::solveqp(H, lb=lb, ub=ub, A=A, Alb=Alb, Aub=Aub)$solution,
  quadprog = quadprog::solve.QP(H, numeric(n), At, b, meq=1)$solution
)


knitr::kable(summary(bm, "relative"), digits=1)

expr	min	lq	mean	median	uq	max	neval
qpmadr	1.0	1.0	1.0	1.0	1.0	1.0	100
quadprog	2.7	2.5	2.5	2.8	2.4	2.5	100

Timings are relative.

C++-interface

The solver is a c++ header-only library and can be used in other packages via the LinkingTo: field