C_constraint function

Conic Constraints

Conic constraints are often written in the form [REMOVE_ME]$Lx + s = rhs [REMOVE_ME_2]$

where $L$ is a $m \times n$ (sparse) matrix and $s \in \mathcal{K}$ are the slack variables restricted to some cone $\mathcal{K}$ which is typically the product of simpler cones $\mathcal{K} = \prod \mathcal{K}_i$. The right hand side $rhs$

is a vector of length $m$.

C_constraint(L, cones, rhs, names = NULL)

as.C_constraint(x, ...)

is.C_constraint(x)

## S3 method for class 'C_constraint'
length(x)

## S3 method for class 'C_constraint'
variable.names(object, ...)

## S3 method for class 'C_constraint'
terms(x, ...)

Arguments

• L: a numeric vector of length $n$ (a single constraint) or a matrix of dimension $m \times n$, where $n$ is the number of objective variables and $m$ is the number of constraints. Matrices can be of class "simple_triplet_matrix" to allow a sparse representation of constraints.

• cones: an object of class "cone" created by the combination, of K_zero, K_lin, K_soc, K_psd, K_expp, K_expd, K_powp or K_powd.

• rhs: a numeric vector giving the right hand side of the constraints.

• names: an optional character vector giving the names of $x$

  (column names of $L$).

• x: an R object.

• ...: further arguments passed to or from other methods (currently ignored).

• object: an R object.

Returns

an object of class "C_constraint" which inherits from "constraint".

Description

Conic constraints are often written in the form

where $L$ is a $m \times n$ (sparse) matrix and $s \in \mathcal{K}$ are the slack variables restricted to some cone $\mathcal{K}$ which is typically the product of simpler cones $\mathcal{K} = \prod \mathcal{K}_i$. The right hand side $rhs$

is a vector of length $m$.

Examples

## minimize:  x1 + x2 + x3
## subject to: 
##   x1 == sqrt(2)
##   ||(x2, x3)|| <= x1
x <- OP(objective = c(1, 1, 1), 
        constraints = C_constraint(L = rbind(rbind(c(1, 0, 0)), 
                                             diag(x=-1, 3)), 
                                   cones = c(K_zero(1), K_soc(3)), 
                                   rhs = c(sqrt(2), rep(0, 3))), 
        types = rep("C", 3),
        bounds =  V_bound(li = 1:3, lb = rep(-Inf, 3)), maximum = FALSE)