R Interface to PIQP Solver

Description

PIQP is an Proximal Interior Point Quadratic Programming solver, which can solve dense and sparse quadratic programs described in described in Schwan, Jiang, Kuhn, and Jones (2023) (https://arxiv.org/abs/2304.00290). Combining an infeasible interior point method with the proximal method of multipliers, the algorithm can handle ill-conditioned convex QP problems without the need for linear independence of the constraints. The solver is written in header only 'C++ 14' leveraging the Eigen library for vectorized linear algebra. For small dense problems, vectorized instructions and cache locality can be exploited more efficiently. Allocation free problem updates and re-solves are also provided.

Author(s)

Balasubramanian Narasimhan, Roland Schwan (C), Yuning Jiang, Daniel Kuhn, Colin N. Jones

See Also

Useful links:

• https://predict-epfl.github.io/piqp-r/

• Report bugs at https://github.com/PREDICT-EPFL/piqp-r/issues

Get dimensions of a PIQP model

Description

Get dimensions of a PIQP model

Usage

get_dims(model, ...)

Arguments

Value

a list with named elements n, p, and m

Get settings of a PIQP model

Description

Get settings of a PIQP model

Usage

get_settings(model, ...)

Arguments

Value

a list of current settings

Convert a plain matrix or simple triplet form matrix to a Matrix::dgCMatrix (implicit) form

Description

Convert a plain matrix or simple triplet form matrix to a Matrix::dgCMatrix (implicit) form

Usage

make_csc_matrix(x)

Arguments

Value

a list of row pointer, column pointer, and values corresponding to a Matrix::dgCMatrix object

Convert a plain matrix or simple triplet form matrix to a Matrix::dsCMatrix (implicit, upper) form

Description

Convert a plain matrix or simple triplet form matrix to a Matrix::dsCMatrix (implicit, upper) form

Usage

make_csc_symm_matrix(m)

Arguments

Value

a list of row pointer, column pointer, and values corresponding to a Matrix::dsCMatrix object

PIQP Solver object

Description

PIQP Solver object

Usage

piqp(
  P = NULL,
  c = NULL,
  A = NULL,
  b = NULL,
  G = NULL,
  h_l = NULL,
  h_u = NULL,
  x_l = NULL,
  x_u = NULL,
  settings = list(),
  backend = c("auto", "sparse", "dense")
)

Arguments

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 piqp contains several methods 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 "piqp_model" with methods solve(), update(), get_settings(), get_dims(), update_settings() which can be used to solve the problem with updated settings / parameters.

Usage

model = piqp(P = NULL, c = NULL, A = NULL, b = NULL, G = NULL,
             h_l = NULL, h_u = NULL, x_l = NULL, x_u = NULL,
             settings = piqp_settings(),
             backend = c("auto", "sparse", "dense"))

solve(model)
update(model, P = NULL, c = NULL, A = NULL, b = NULL, G = NULL,
       h_l = NULL, h_u = NULL, x_l = NULL, x_u = NULL)
get_settings(model)
get_dims(model)
update_settings(model, new_settings = piqp_settings())

See Also

solve_piqp(), piqp_settings()

Examples

## example, adapted from PIQP documentation
library(piqp)
library(Matrix)

P <- Matrix(c(6., 0.,
              0., 4.), 2, 2, sparse = TRUE)
c <- c(-1., -4.)
A <- Matrix(c(1., -2.), 1, 2, sparse = TRUE)
b <- c(1.)
G <- Matrix(c(1., 2., -1., 0.), 2, 2, sparse = TRUE)
h_u <- c(0.2, -1.)
x_l <- c(-1., -Inf)
x_u <- c(1., Inf)

settings <- list(verbose = TRUE)

model <- piqp(P, c, A, b, G, h_u = h_u, x_l = x_l, x_u = x_u, settings = settings)

# Solve
res <- solve(model)
res$x

# Define new data
A_new <- Matrix(c(1., -3.), 1, 2, sparse = TRUE)
h_u_new <- c(2., 1.)

# Update model and solve again
update(model, A = A_new, h_u = h_u_new)
res <- solve(model)
res$x

The PIQP Solver Model Class

Description

An S7 class wrapping the PIQP C++ Solver. Users will never need to directly create instances of this class and should use the more user-friendly functions piqp() and solve_piqp().

Usage

piqp_model(solver_ptr = NULL, dims = list(), dense_backend = logical(0))

Arguments

Settings parameters with default values and types in parenthesis

Description

Settings parameters with default values and types in parenthesis

Usage

piqp_settings(
  rho_init = 1e-06,
  delta_init = 1e-04,
  eps_abs = 1e-08,
  eps_rel = 1e-09,
  check_duality_gap = TRUE,
  eps_duality_gap_abs = 1e-08,
  eps_duality_gap_rel = 1e-09,
  infeasibility_threshold = 0.9,
  reg_lower_limit = 1e-10,
  reg_finetune_lower_limit = 1e-13,
  reg_finetune_primal_update_threshold = 7L,
  reg_finetune_dual_update_threshold = 7L,
  max_iter = 250L,
  max_factor_retires = 10L,
  preconditioner_scale_cost = FALSE,
  preconditioner_reuse_on_update = FALSE,
  preconditioner_iter = 10L,
  tau = 0.99,
  iterative_refinement_always_enabled = FALSE,
  iterative_refinement_eps_abs = 1e-12,
  iterative_refinement_eps_rel = 1e-12,
  iterative_refinement_max_iter = 10L,
  iterative_refinement_min_improvement_rate = 5,
  iterative_refinement_static_regularization_eps = 1e-08,
  iterative_refinement_static_regularization_rel = .Machine$double.eps^2,
  verbose = FALSE,
  compute_timings = FALSE
)

Arguments

Value

a list containing the settings parameters.

PIQP Solver

Description

Solves

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

s.t.

A x = b

h_l \leq G x \leq h_u

x_l \leq x \leq x_u

for real matrices P (nxn, positive semidefinite), A (pxn) with p number of equality constraints, and G (mxn) with m number of inequality constraints

Usage

solve_piqp(
  P = NULL,
  c = NULL,
  A = NULL,
  b = NULL,
  G = NULL,
  h_l = NULL,
  h_u = NULL,
  x_l = NULL,
  x_u = NULL,
  settings = list(),
  backend = c("auto", "sparse", "dense")
)

Arguments

Value

A list with elements solution elements

References

Schwan, R., Jiang, Y., Kuhn, D., Jones, C.N. (2023). “PIQP: A Proximal Interior-Point Quadratic Programming Solver.” doi:10.48550/arXiv.2304.00290

See Also

piqp(), piqp_settings() and the underlying PIQP documentation: https://predict-epfl.github.io/piqp/

Examples

## example, adapted from PIQP documentation
library(piqp)
library(Matrix)

P <- Matrix(c(6., 0.,
              0., 4.), 2, 2, sparse = TRUE)
c <- c(-1., -4.)
A <- Matrix(c(1., -2.), 1, 2, sparse = TRUE)
b <- c(1.)
G <- Matrix(c(1., 2., -1., 0.), 2, 2, sparse = TRUE)
h_u <- c(0.2, -1.)
x_l <- c(-1., -Inf)
x_u <- c(1., Inf)

settings <- list(verbose = TRUE)

# Solve with PIQP
res <- solve_piqp(P, c, A, b, G, h_u = h_u, x_l = x_l, x_u = x_u, settings = settings)
res$x

Return the solver status description string

Description

Return the solver status description string

Usage

status_description(code)

Arguments

Value

a status description string

Examples

status_description(1) ## for solved problem
status_description(-1) ## for max iterations limit reached

Update settings of a PIQP model

Description

Update settings of a PIQP model

Usage

update_settings(model, ...)

Arguments

Value

invisible NULL