R: SCS - Splitting Conic Solver

scs {scs} | R Documentation

## 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

`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
`P` | a symmetric positive semidefinite matrix, default `NULL`
`cone` | a list giving the cone sizes
`initial` | a named list (warm start solution) of three elements: `x` (length = `length(obj)`), `y` (length = `nrow(A)`), and `s` (length = `nrow(A)`), default NULL indicating no warm start.
`control` | a list giving the control parameters. For more information see README.

### 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 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
| `z` | 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)
| `bsize` | integer | 1 | size of box cone
| `bl` | numeric | bsize-1 | lower limit for box cone
| `bu` | numeric | bsize-1 | upper limit for box cone
| `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

### Value

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

### 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

[Package scs version 3.0-0 Index]