Package 'ECOSolveR'

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

c	the coefficients of the objective function; the length of this determines the number of variables $n$ in the problem.
G	the inequality constraint matrix in one of three forms: a plain matrix, simple triplet matrix, or compressed column format, e.g. dgCMatrix-class. Can also be NULL
h	the right hand size of the inequality constraint. Can be empty numeric vector.
dims	is a list of three named elements: dims['l'] an integer specifying the dimension of positive orthant cone, dims['q'] an integer vector specifying dimensions of second-order cones, dims['e'] an integer specifying the number of exponential cones
A	the optional equality constraint matrix in one of three forms: a plain matrix, simple triplet matrix, or compressed column format, e.g. dgCMatrix-class. Can be NULL
b	the right hand side of the equality constraint, must be specified if $A$ is. Can be empty numeric vector.
bool_vars	the indices of the variables, 1 through $n$, that are boolean; that is, they are either present or absent in the solution
int_vars	the indices of the variables, 1 through $n$, that are integers
control	is a named list that controls various optimization parameters; see ecos.control.

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

---

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

maxit	the maximum number of iterations for ecos, default 100L
feastol	the tolerance on the primal and dual residual, default 1e-8
reltol	the relative tolerance on the duality gap, default 1e-8
abstol	the absolute tolerance on the duality gap, default 1e-8
feastol_inacc	the tolerance on the primal and dual residual if reduced precisions, default 1e-4
abstol_inacc	the absolute tolerance on the duality gap if reduced precision, default 5e-5
reltol_inacc	the relative tolerance on the duality gap if reduced precision, default 5e-5
verbose	verbosity level, default 0L. A verbosity level of 1L will show more detail, but clutter session transcript.
mi_max_iters	the maximum number of branch and bound iterations (mixed integer problems only), default 1000L
mi_int_tol	the integer tolerence (mixed integer problems only), default 1e-4
mi_abs_eps	the absolute tolerance between upper and lower bounds (mixed integer problems only), default 1e-6
mi_rel_eps	the relative tolerance, $(U-L)/L$, between upper and lower bounds (mixed integer problems only), default 1e-6

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

x	a matrix or a simple triplet form matrix

Value

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

---