ECOSolveR: Embedded Conic Solver in R

Description

ECOSolveR is a wrapper around the ecos library. Please see the examples and documentation for the function ECOS_csolve.

Author(s)

Maintainer: Balasubramanian Narasimhan naras@stat.Stanford.EDU

Authors:

• Anqi Fu anqi.fu.1987@gmail.com

Other contributors:

• Florian Schwendinger FlorianSchwendinger@gmx.at [contributor]

• Martin Maechler maechler@stat.math.ethz.ch [contributor]

References

https://github.com/embotech/ecos

See Also

Useful links:

• https://bnaras.github.io/ECOSolveR/

• Report bugs at https://github.com/bnaras/ECOSolveR/issues

Clean up an ECOS workspace

Description

Frees the C-level ECOS workspace. After this call the workspace external pointer is invalidated and cannot be used for further solves or updates. It is safe to call this more than once.

Usage

ECOS_cleanup(workspace)

Arguments

Value

NULL, invisibly.

See Also

ECOS_setup, ECOS_solve, ECOS_update

Solve a conic optimization problem

Description

The function ECOS_csolve is a wrapper around the ecos csolve C function. Conic constraints are specified using the G and h parameters and can be NULL and zero length vector respectively indicating an absence of conic constraints. Similarly, equality constraints are specified via A and b parameters with NULL and empty vector values representing a lack of such constraints. At most one of the pair (G , h) or (A, b) is allowed to be absent.

Usage

ECOS_csolve(
  c = numeric(0),
  G = NULL,
  h = numeric(0),
  dims = list(l = integer(0), q = NULL, e = integer(0)),
  A = NULL,
  b = numeric(0),
  bool_vars = integer(0),
  int_vars = integer(0),
  control = ecos.control()
)

Arguments

Value

a list of 8 named items

x

primal variables

y

dual variables for equality constraints

s

slacks for Gx + s <= h, s \in K

z

dual variables for inequality constraints s \in K

infostring

gives information about the status of solution

retcodes

a named integer vector containing four elements

exitflag

0=ECOS_OPTIMAL, 1=ECOS_PINF, 2=ECOS_DINF, 10=ECOS_INACC_OFFSET, -1=ECOS_MAXIT, -2=ECOS_NUMERICS, -3=ECOS_OUTCONE, -4=ECOS_SIGINT, -7=ECOS_FATAL. See ECOS_exitcodes

.

iter

the number of iterations used

mi_iter

the number of iterations for mixed integer problems

numerr

a non-zero number if a numeric error occurred

summary

a named numeric vector containing

pcost

value of primal objective

dcost

value of dual objective

pres

primal residual on inequalities and equalities

dres

dual residual

pinf

primal infeasibility measure

dinf

dual infeasibility measure

pinfres

primal infeasibility residual

dinfres

dual infeasibility residual

gap

duality gap

relgap

relative duality gap

r0

Unknown at the moment to this R package maintainer.

timing

a named numeric vector of timing information consisting of

runtime

the total runtime in ecos

tsetup

the time for setup of the problem

tsolve

the time to solve the problem

Details

A call to this function will solve the problem: minimize c^Tx, subject to Ax = b, and h - G*x \in K.

Variables can be constrained to be boolean (1 or 0) or integers. This is indicated by specifying parameters bool_vars and/or int_vars respectively. If so indicated, the solutions will be found using a branch and bound algorithm.

Examples

## githubIssue98
cat("Basic matrix interface\n")
Gmat <- matrix(c(0.416757847405471, 2.13619609566845, 1.79343558519486, 0, 0,
                 0, 0, -1, 0, 0, 0, 0.056266827226329, -1.64027080840499, 0.841747365656204,
                 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0.416757847405471, 2.13619609566845,
                 1.79343558519486, 0, 0, 0, -1, 0, 0, 0, 0, 0.056266827226329, -1.64027080840499,
                 0.841747365656204, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0), ncol = 5L)
c <- as.numeric(c(0, 0, 0, 0, 1))
h <- as.numeric(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
dims <- list(l = 6L, q = 5L, e = 0L)
ECOS_csolve(c = c, G = Gmat, h = h,
           dims = dims,
           A = NULL, b = numeric(0))

cat("Simple Triplet Matrix interface, if you have package slam\n")
if (requireNamespace("slam")) {

  ECOS_csolve(c = c, G = slam::as.simple_triplet_matrix(Gmat), h = h,
              dims = dims,
              A = NULL, b = numeric(0))
}

if (requireNamespace("Matrix")) {
   ECOS_csolve(c = c, G = Matrix::Matrix(Gmat), h = h,
               dims = dims,
               A = NULL, b = numeric(0))
}

## Larger problems using saved data can be found in the test suite.
## Here is one
if (requireNamespace("Matrix")) {
  MPC01 <- readRDS(system.file("testdata", "MPC01_1.RDS", package = "ECOSolveR"))
  G <- Matrix::sparseMatrix(x = MPC01$Gpr, i = MPC01$Gir, p = MPC01$Gjc,
                            dims = c(MPC01$m, MPC01$n), index1 = FALSE)
  h <- MPC01$h
  dims <- lapply(list(l = MPC01$l, q=MPC01$q, e=MPC01$e), as.integer)
  retval <- ECOS_csolve(c = MPC01$c, G=G, h = h, dims = dims, A = NULL, b = NULL,
                        control = ecos.control(verbose=1L))
  retval$retcodes
  retval$infostring
  retval$summary
}

ECOS solver exit codes

Description

A two-column data frame consisting of the code and description for the ECOS solver with ECOS symbolic code names as row names

Set up an ECOS workspace for multi-step solving

Description

Creates an ECOS workspace that can be solved, updated with new numerical data, and solved again without repeating the expensive symbolic analysis phase. This is useful for parametric optimization, model predictive control, and other settings where the problem structure stays the same but data changes.

Usage

ECOS_setup(
  c,
  G,
  h,
  dims = list(l = integer(0), q = NULL, e = integer(0)),
  A = NULL,
  b = numeric(0),
  control = ecos.control()
)

Arguments

Value

an external pointer of class "ecos_workspace". Must eventually be freed via ECOS_cleanup or R garbage collection.

See Also

ECOS_solve, ECOS_update, ECOS_cleanup, ECOS_csolve

Solve an ECOS workspace

Description

Calls ECOS_solve on an existing workspace created by ECOS_setup. The workspace can be solved multiple times, optionally with ECOS_update calls in between to change numerical data.

Usage

ECOS_solve(workspace, control = NULL)

Arguments

Value

the same result list as ECOS_csolve.

See Also

ECOS_setup, ECOS_update, ECOS_cleanup

Update numerical data in an ECOS workspace

Description

Replaces numerical values in an existing ECOS workspace without repeating symbolic analysis. The sparsity structure must remain the same; only the non-zero values of G and A, and the dense vectors c, h, b can be updated. Pass NULL for any argument to leave it unchanged.

Usage

ECOS_update(workspace, Gpr = NULL, Apr = NULL, c = NULL, h = NULL, b = NULL)

Arguments

Value

the workspace object, invisibly.

See Also

ECOS_setup, ECOS_solve, ECOS_cleanup

Return the default optimization parameters for ECOS

Description

This is used to control the behavior of the underlying optimization code.

Usage

ecos.control(
  maxit = 100L,
  feastol = 1e-08,
  reltol = 1e-08,
  abstol = 1e-08,
  feastol_inacc = 1e-04,
  abstol_inacc = 5e-05,
  reltol_inacc = 5e-05,
  verbose = 0L,
  mi_max_iters = 1000L,
  mi_int_tol = 1e-04,
  mi_abs_eps = 1e-06,
  mi_rel_eps = 1e-06
)

Arguments

Value

a list with the following elements:

FEASTOL

the tolerance on the primal and dual residual, parameter feastol

ABSTOL

the absolute tolerance on the duality gap, parameter abstol

RELTOL

the relative tolerance on the duality gap, parameter reltol

FEASTOL_INACC

the tolerance on the primal and dual residual if reduced precisions, parameter feastol_inacc

ABSTOL_INACC

the absolute tolerance on the duality gap if reduced precision, parameter abstol_inacc

RELTOL_INACC

the relative tolerance on the duality gap if reduced precision, parameter reltol_inacc

MAXIT

the maximum number of iterations for ecos, parameter maxit

MI_MAX_ITERS

the maximum number of branch and bound iterations (mixed integer problems only), parameter mi_max_iters

MI_INT_TOL

the integer tolerence (mixed integer problems only), parameter mi_int_tol

MI_ABS_EPS

the absolute tolerance between upper and lower bounds (mixed integer problems only), parameter mi_abs_eps

MI_REL_EPS

the relative tolerance, (U-L)/L, between upper and lower bounds (mixed integer problems only), parameter mi_rel_eps

VERBOSE

verbosity level, parameter verbose

Convert a plain matrix or simple triplet form matrix to a [Matrix::dgCMatrix-class] (implicit) form

Description

Convert a plain matrix or simple triplet form matrix to a [Matrix::dgCMatrix-class] (implicit) form

Usage

make_csc_matrix(x)

Arguments

Value

a list of row pointer, column pointer, and values corresponding to a [Matrix::dgCMatrix-class] object

Print method for ECOS workspace objects

Description

Print method for ECOS workspace objects

Usage

## S3 method for class 'ecos_workspace'
print(x, ...)

Arguments

Value

x, invisibly.