SCS - Splitting Conic Solver

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Description

Solves convex cone programs via operator splitting.

Usage

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scs(A, b, obj, cone, control = list(max_iters = 2500L, normalize = TRUE,
  verbose = FALSE, cg_rate = 2, scale = 5, rho_x = 0.001, alpha = 1.5, eps =
  1e-06))

Arguments

A

a matrix of constraint coefficients. NOTE: The rows of matrix A have to be ordered according to the order given in subsection “Allowed cone parameters”. For more information see README.

b

a numeric vector giving the primal constraints

obj

a numeric vector giving the primal objective

cone

a list giving the cone sizes

control

a list giving the control parameters. For more information see README.

Details

A more detailed description can be found in the README file.

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 second-order cone third, rows corresponding to positive semidefinite cones fourth, rows corresponding to exponential cones fifth 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)

  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

Parameter Type Length Description
f integer 1 number of primal zero cones (dual free cones),
which corresponds to the primal equality constraints
l integer 1 number of linear cones (non-negative cones)
q integer ≥q1 vector of second-order cone sizes
s integer ≥q1 vector of positive semidefinite cone sizes
ep integer 1 number of primal exponential cones
ed integer 1 number of dual exponential cones
p numeric ≥q1 vector of primal/dual power cone parameters

Allowed control parameters are

Parameter Type Description Default
max_iters integer giving the maximum number of iterations 2500
normalize boolean heuristic data rescaling TRUE
verbose boolean write out progress FALSE
cg_rate numeric for indirect, tolerance goes down like \frac{1}{iter}^{cg\_rate} 2
scale numeric if normalized, rescales by this factor 5
rho_x numeric x equality constraint scaling 1e-3
alpha numeric relaxation parameter 1.5
eps numeric convergence tolerance 1e-3

Value

list of solution vectors x, y, s and information about run

Examples

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

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