solve_piqp {piqp}

PIQP Solver

Description

Solves

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

s.t.

A x = b

G x \leq h

x_{lb} \leq x \leq x_{ub}

for real matrices P (nxn, positive semidefinite), A (pxn) with m 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 = NULL,
  x_lb = NULL,
  x_ub = NULL,
  settings = list(),
  backend = c("auto", "sparse", "dense")
)

Arguments

P

dense or sparse matrix of class dgCMatrix or coercible into such, must be positive semidefinite

c

numeric vector

A

dense or sparse matrix of class dgCMatrix or coercible into such

b

numeric vector

G

dense or sparse matrix of class dgCMatrix or coercible into such

h

numeric vector

x_lb

a numeric vector of lower bounds, default NULL indicating -Inf for all variables, otherwise should be number of variables long

x_ub

a numeric vector of upper bounds, default NULL indicating Inf for all variables, otherwise should be number of variables long

settings

list with optimization parameters, empty by default; see piqp_settings() for a comprehensive list of parameters that may be used

backend

which backend to use, if auto and P, A or G are sparse then sparse backend is used ("auto", "sparse" or "dense") ("auto")

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 <- c(0.2, -1.)
x_lb <- c(-1., -Inf)
x_ub <- c(1., Inf)

settings <- list(verbose = TRUE)

# Solve with PIQP
res <- solve_piqp(P, c, A, b, G, h, x_lb, x_ub, settings)
res$x