Q_constraint function

Quadratic Constraints

Quadratic constraints are typically of the form [REMOVE_ME]$\frac{1}{2}x^{\top}Q_ix + L_i x \leq rhs_i [REMOVE_ME_2]$

where $Q_i$ is the $i$th of $m$ (sparse) matrices (all of dimension $n \times n$) giving the coefficients of the quadratic part of the equation. The $m \times n$ (sparse) matrix $L$

holds the coefficients of the linear part of the equation and $L_i$

refers to the $i$th row. The right hand side of the constraints is represented by the vector $rhs$.

Q_constraint(Q, L, dir, rhs, names = NULL)

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

as.Q_constraint(x)

is.Q_constraint(x)

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

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

Arguments

• Q: a list of (sparse) matrices representing the quadratic part of each constraint.

• 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.

• dir: a character vector with the directions of the constraints. Each element must be one of "<=", ">=" or "==".

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

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

  (row/column names of $Q$, column names of $A$).

• object: an R object.

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

• x: an R object.

Returns

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

Description

Quadratic constraints are typically of the form

where $Q_i$ is the $i$th of $m$ (sparse) matrices (all of dimension $n \times n$) giving the coefficients of the quadratic part of the equation. The $m \times n$ (sparse) matrix $L$

holds the coefficients of the linear part of the equation and $L_i$

refers to the $i$th row. The right hand side of the constraints is represented by the vector $rhs$.

Author(s)

Stefan Theussl