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Title:

Quadratic Programming Solver using the 'OSQP' Library

Version:

1.0.0

Date:

2026-02-27

file COPYRIGHT

Description:

Provides bindings to the 'OSQP' solver. The 'OSQP' solver is a numerical optimization package for solving convex quadratic programs written in 'C' and based on the alternating direction method of multipliers. See <doi:10.48550/arXiv.1711.08013> for details.

License:

Apache License 2.0 | file LICENSE

SystemRequirements:

C++17, GNU make

Imports:

Rcpp (≥ 0.12.14), methods, Matrix (≥ 1.6.1), S7, cli

LinkingTo:

Rcpp

RoxygenNote:

7.3.3

Collate:

'RcppExports.R' 'osqp-package.R' 'sparse.R' 'solve.R' 'osqp.R' 'params.R'

NeedsCompilation:

yes

VignetteBuilder:

knitr

Suggests:

knitr, rmarkdown, slam, testthat

Encoding:

UTF-8

BugReports:

https://github.com/osqp/osqp-r/issues

URL:

https://osqp.org

Packaged:

2026-02-28 16:07:45 UTC; naras

Author:

Bartolomeo Stellato [aut, ctb, cph], Goran Banjac [aut, ctb, cph], Paul Goulart [aut, ctb, cph], Stephen Boyd [aut, ctb, cph], Eric Anderson [ctb], Vineet Bansal [aut, ctb], Balasubramanian Narasimhan [cre, aut]

Maintainer:

Balasubramanian Narasimhan <naras@stanford.edu>

Repository:

CRAN

Date/Publication:

2026-03-01 10:00:02 UTC

OSQP Model Class (S7)

Description

An S7 class representing an OSQP solver model. Methods are accessed via computed properties using the @ operator.

Usage

OSQP_Model(work)

OSQP Solver object

Description

OSQP Solver object

Usage

osqp(P = NULL, q = NULL, A = NULL, l = NULL, u = NULL, pars = osqpSettings())

Arguments

P, A

sparse matrices of class dgCMatrix or coercible into such, with P positive semidefinite. (In the interest of efficiency, only the upper triangular part of P is used)

q, l, u

Numeric vectors, with possibly infinite elements in l and u

pars

list with optimization parameters, conveniently set with the function osqpSettings. For model@UpdateSettings(newPars) only a subset of the settings can be updated once the problem has been initialized.

Details

Allows one to solve a parametric problem with for example warm starts between updates of the parameter, c.f. the examples. The object returned by osqp contains several computed properties (accessed via @) which can be used to either update/get details of the problem, modify the optimization settings or attempt to solve the problem.

Value

An S7 object of class "OSQP_Model" with computed properties that return methods.

Usage

model = osqp(P=NULL, q=NULL, A=NULL, l=NULL, u=NULL, pars=osqpSettings())

model@Solve()
model@Update(q = NULL, l = NULL, u = NULL, Px = NULL, Px_idx = NULL, Ax = NULL, Ax_idx = NULL)
model@GetParams()
model@GetDims()
model@UpdateSettings(newPars = list())

model@GetData(element = c("P", "q", "A", "l", "u"))
model@WarmStart(x=NULL, y=NULL)
model@ColdStart()

print(model)

Method Arguments

element: a string with the name of one of the matrices / vectors of the problem
newPars: list with optimization parameters

Examples

## example, adapted from OSQP documentation
library(Matrix)

P <- Matrix(c(11., 0.,
              0., 0.), 2, 2, sparse = TRUE)
q <- c(3., 4.)
A <- Matrix(c(-1., 0., -1., 2., 3.,
              0., -1., -3., 5., 4.)
              , 5, 2, sparse = TRUE)
u <- c(0., 0., -15., 100., 80)
l <- rep_len(-Inf, 5)

settings <- osqpSettings(verbose = FALSE)

model <- osqp(P, q, A, l, u, settings)

# Solve
res <- model@Solve()

# Define new vector
q_new <- c(10., 20.)

# Update model and solve again
model@Update(q = q_new)
res <- model@Solve()

Settings for OSQP

Description

For further details please consult the OSQP documentation: https://osqp.org/

Usage

osqpSettings(
  rho = 0.1,
  rho_is_vec = TRUE,
  sigma = 1e-06,
  max_iter = 4000L,
  eps_abs = 0.001,
  eps_rel = 0.001,
  eps_prim_inf = 1e-04,
  eps_dual_inf = 1e-04,
  alpha = 1.6,
  linsys_solver = c(OSQP_DIRECT_SOLVER = 1L),
  delta = 1e-06,
  polishing = FALSE,
  polish_refine_iter = 3L,
  verbose = TRUE,
  scaled_termination = FALSE,
  check_termination = 25L,
  check_dualgap = TRUE,
  warm_starting = TRUE,
  scaling = 10L,
  adaptive_rho = 1L,
  adaptive_rho_interval = 50L,
  adaptive_rho_tolerance = 5,
  adaptive_rho_fraction = 0.4,
  cg_max_iter = 20L,
  cg_tol_reduction = 10L,
  cg_tol_fraction = 0.15,
  cg_precond = c(OSQP_DIAGONAL_PRECONDITIONER = 1L),
  profiler_level = 0L,
  time_limit = 1e+10,
  polish = NULL,
  warm_start = NULL
)

Arguments

rho

ADMM step rho

rho_is_vec

boolean, whether rho is treated as a vector (per-constraint) or scalar

sigma

ADMM step sigma

max_iter

maximum iterations

eps_abs

absolute convergence tolerance

eps_rel

relative convergence tolerance

eps_prim_inf

primal infeasibility tolerance

eps_dual_inf

dual infeasibility tolerance

alpha

relaxation parameter

linsys_solver

which linear systems solver to use, 1=OSQP_DIRECT_SOLVER (QDLDL), 2=OSQP_INDIRECT_SOLVER

delta

regularization parameter for polishing

polishing

boolean, polish ADMM solution

polish_refine_iter

iterative refinement steps in polishing

verbose

boolean, write out progress

scaled_termination

boolean, use scaled termination criteria

check_termination

integer, check termination interval. If 0, termination checking is disabled

check_dualgap

boolean, check duality gap termination criteria

warm_starting

boolean, warm start

scaling

heuristic data scaling iterations. If 0, scaling disabled

adaptive_rho

integer, rho adaptation strategy: 0=disabled, 1=iterations, 2=time, 3=KKT error

adaptive_rho_interval

Number of iterations between rho adaptations rho. If 0, it is automatic

adaptive_rho_tolerance

Tolerance X for adapting rho. The new rho has to be X times larger or 1/X times smaller than the current one to trigger a new factorization

adaptive_rho_fraction

Interval for adapting rho (fraction of the setup time)

cg_max_iter

maximum number of CG iterations (indirect solver only)

cg_tol_reduction

integer, number of consecutive zero CG iterations before the tolerance gets halved (indirect solver only)

cg_tol_fraction

CG tolerance fraction (indirect solver only)

cg_precond

preconditioner for CG method (indirect solver only): 0=none, 1=diagonal (Jacobi)

profiler_level

integer, level of detail for profiler annotations (0=off)

time_limit

run time limit in seconds (1e10 effectively disables)

polish

Deprecated. Use polishing instead.

warm_start

Deprecated. Use warm_starting instead.

Sparse Quadratic Programming Solver

Description

Solves

arg\min_x 0.5 x'P x + q'x

s.t.

l_i < (A x)_i < u_i

for real matrices P (nxn, positive semidefinite) and A (mxn) with m number of constraints

Usage

solve_osqp(
  P = NULL,
  q = NULL,
  A = NULL,
  l = NULL,
  u = NULL,
  pars = osqpSettings()
)

Arguments

P, A

sparse matrices of class dgCMatrix or coercible into such, with P positive semidefinite. Only the upper triangular part of P will be used.

q, l, u

Numeric vectors, with possibly infinite elements in l and u

pars

list with optimization parameters, conveniently set with the function osqpSettings

Value

A list with elements x (the primal solution), y (the dual solution), prim_inf_cert, dual_inf_cert, and info.

References

Stellato, B., Banjac, G., Goulart, P., Bemporad, A., Boyd and S. (2018). “OSQP: An Operator Splitting Solver for Quadratic Programs.” ArXiv e-prints. 1711.08013.

Examples

library(osqp)
## example, adapted from OSQP documentation
library(Matrix)

P <- Matrix(c(11., 0.,
              0., 0.), 2, 2, sparse = TRUE)
q <- c(3., 4.)
A <- Matrix(c(-1., 0., -1., 2., 3.,
              0., -1., -3., 5., 4.)
              , 5, 2, sparse = TRUE)
u <- c(0., 0., -15., 100., 80)
l <- rep_len(-Inf, 5)

settings <- osqpSettings(verbose = TRUE)

# Solve with OSQP
res <- solve_osqp(P, q, A, l, u, settings)
res$x

OSQP Model Class (S7)

Description

Usage

OSQP Solver object

Description

Usage

Arguments

Details

Value

Usage

Method Arguments

See Also

Examples

Settings for OSQP

Description

Usage

Arguments

Sparse Quadratic Programming Solver

Description

Usage

Arguments

Value

References

See Also

Examples