Package {scs}

SCS - Splitting Conic Solver

Description

Solves convex cone programs via operator splitting.

Usage

scs(A, b, obj, P = NULL, cone, initial = NULL, control = scs_control())

Arguments

Details

Important Note

The order of the rows in matrix A has to correspond to the order given in the table “Cone Arguments”, which means means rows corresponding to primal zero cones should be first, rows corresponding to non-negative cones second, rows corresponding to box cones third, rows corresponding to second-order cones fourth, rows corresponding to positive semidefinite cones fifth, rows corresponding to complex positive semidefinite cones sixth, rows corresponding to exponential cones seventh and rows corresponding to power cones at last.

SCS can solve

1. linear programs (LPs)

2. second-order cone programs (SOCPs)

3. semidefinite programs (SDPs), real and complex

4. exponential cone programs (ECPs)

5. power cone programs (PCPs)

6. problems with any combination of cones, which can be defined by the parameters listed in the subsection “Allowed cone parameters”

Allowed cone parameters are

A real positive semidefinite cone of order k occupies k(k+1)/2 rows (lower triangle, column-wise, off-diagonal entries scaled by \sqrt{2}); a complex positive semidefinite cone of order k occupies k^2 rows (real and imaginary parts of the lower triangle, same scaling). The experimental spectral cones of the SCS C library (log-determinant, nuclear norm, \ell_1, sum of largest eigenvalues) are not compiled into this package. The redundant length fields qsize, ssize, cssize and psize are accepted for backward compatibility and must equal the length of the vector they describe.

Return information

info is a list with the elements iter, status, lin_sys_solver, status_val, scale_updates, pobj, dobj, res_pri, res_dual, gap, res_infeas, res_unbdd_a, res_unbdd_p, setup_time, solve_time (milliseconds), scale, comp_slack, rejected_accel_steps, accepted_accel_steps, aa_stats, lin_sys_time, cone_time and accel_time (milliseconds). status_val is the SCS exit flag: 1 solved, 2 solved inaccurately, -1 unbounded, -2 infeasible, -4 failed, -5 interrupted, -6 unbounded inaccurately, -7 infeasible inaccurately. aa_stats is a list of Anderson acceleration diagnostics: iter, n_accept, n_reject_lapack, n_reject_rank0, n_reject_nonfinite, n_reject_weight_cap, n_safeguard_reject, last_rank, last_aa_norm (NaN if no acceleration step was attempted) and last_regularization.

Value

A list with the solution vectors x, y, s and a list info describing the run, see section “Return information”.

Examples

A <- matrix(c(1, 1), ncol=1)
b <- c(1, 1)
obj <- 1
cone <- list(z = 2)
control <- list(eps_rel = 1e-3, eps_abs = 1e-3, max_iters = 50)
sol <- scs(A = A, b = b, obj = obj, cone = cone, control = control)
sol

SCS Control Arguments

Description

Details to the control parameters. The defaults are those of the bundled SCS C library (see scs_version), except verbose, which is FALSE here.

Usage

scs_control(
  max_iters = 100000L,
  eps_rel = 1e-04,
  eps_abs = 1e-04,
  eps_infeas = 1e-07,
  alpha = 1.5,
  rho_x = 1e-06,
  scale = 0.1,
  verbose = FALSE,
  normalize = TRUE,
  warm_start = FALSE,
  acceleration_lookback = 10L,
  acceleration_interval = 5L,
  adaptive_scale = TRUE,
  write_data_filename = NULL,
  log_csv_filename = NULL,
  time_limit_secs = 0,
  adaptive_diag_scale = TRUE,
  acceleration_type_1 = TRUE,
  acceleration_regularization = 1e-08,
  acceleration_relaxation = 1
)

Arguments

Value

a list containing the control parameters.

Version of the Bundled SCS Library

Description

Returns the version string of the SCS C library compiled into this package.

Usage

scs_version()

Value

a character string, for example "3.3.1".

Examples

scs_version()