naginterfaces.library.opt.handle_​set_​group

naginterfaces.library.opt.handle_set_group(handle, gtype, idgroup, group=None)

handle_set_group is a part of the NAG optimization modelling suite and modifies a model by either adding a new, or replacing, or deleting an existing quadratic or rotated quadratic cone constraint.

For full information please refer to the NAG Library document for e04rb

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/e04/e04rbf.html

Parameters

handleHandle

The handle to the problem. It needs to be initialized (e.g., by handle_init()) and must not be changed between calls to the NAG optimization modelling suite.

gtypestr

The type of the cone constraint. $gtype$ is case insensitive.

$gtype=\text{'QUAD'}$ or $\text{'Q'}$

The group defines a quadratic cone.

$gtype=\text{'RQUAD'}$ or $\text{'R'}$

The group defines a rotated quadratic cone.

idgroupint

$idgroup=0$

A new cone constraint is created.

$idgroup>0$

$i$, the ID number of the existing constraint to be deleted or replaced.

groupNone or int, array-like, shape $\left(\text{lgroup}\right)$, optional

$G^i$, the indices of the variables in the constraint. If $\text{lgroup}=0$, $group$ is not referenced.

Returns

idgroupint

If $idgroup=0$ on entry, the ID number of the new cone constraint is returned. By definition, this is the number of cone constraints already defined plus one. Otherwise, $idgroup$ remains unchanged.

Raises

NagValueError

(errno $1$)

$handle$ has not been initialized.

(errno $1$)

$handle$ does not belong to the NAG optimization modelling suite, has not been initialized properly or is corrupted.

(errno $1$)

$handle$ has not been initialized properly or is corrupted.

(errno $2$)

The problem cannot be modified right now, the solver is running.

(errno $4$)

On entry, $idgroup=⟨value⟩$.

The given $idgroup$ does not match with any cone constraint already defined.

(errno $5$)

On entry, $\text{lgroup}=⟨value⟩$.

Constraint: $\text{lgroup}\ge 0$.

(errno $5$)

On entry, $gtype=⟨value⟩$ and $\text{lgroup}=⟨value⟩$.

Constraint: if $gtype=\text{'QUAD'}$ or $\text{'Q'}$, $\text{lgroup}=0$ or $\text{lgroup}\ge 2$.

(errno $5$)

On entry, $gtype=⟨value⟩$ and $\text{lgroup}=⟨value⟩$.

Constraint: if $gtype=\text{'RQUAD'}$ or $\text{'R'}$, $\text{lgroup}=0$ or $\text{lgroup}\ge 3$.

(errno $6$)

On entry, $gtype=⟨value⟩$.

Constraint: $gtype=\text{'QUAD'}$, $\text{'Q'}$, $\text{'RQUAD'}$ or $\text{'R'}$.

(errno $7$)

On entry, $idgroup=⟨value⟩$.

Constraint: $idgroup\ge 0$.

(errno $8$)

On entry, $k=⟨value⟩$, $group[k-1]=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $1\le group[k-1]\le n$.

(errno $9$)

On entry, $group[i-1]=group[j-1]=⟨value⟩$ for $i=⟨value⟩$ and $j=⟨value⟩$.

Constraint: elements in $group$ cannot repeat.

Notes

After the $handle$ has been initialized (e.g., handle_init() has been called), handle_set_group may be used to edit a model by adding, replacing, or deleting a cone constraint $i$ of dimension $m_i$. The supported cones are quadratic cone and rotated quadratic cone, also known as second-order cones, which are defined as follows:

• Quadratic cone:

  $$K_q^{m_i}:=\{z=(z_1,z_2,\dots ,z_{m_i})\in R^{m_i}\text{:}{z}_1^2\ge \sum _{j=2}^{m_i}{z}_j^2\text{,}{z}_1\ge 0\}\text{.}$$

• Rotated quadratic cone:

  $$K_r^{m_i}:=\{z=(z_1,z_2,\dots ,z_{m_i})\in R^{m_i}\text{:}2z_1{z}_2\ge \sum _{j=3}^{m_i}{z}_j^2\text{,}{z}_1\ge 0\text{,}{z}_2\ge 0\}\text{.}$$

The cone constraint is defined by its type and a subset (group) of variables. Let index set $G^i\subseteq \{1,2,\dots ,n\}$ denote variable indices, then $x_{G^i}$ will denote the subvector of variables $x\in R^n$.

For example, if $m_i=3$ and $G^i=\{4,1,2\}$, then a quadratic cone constraint

$$x_{G^i}=(x_4,x_1,x_2)\in K_q^3$$

implies the inequality constraints

$$x_4^2\ge x_1^2+x_2^2\text{,}{x}_4\ge 0\text{.}$$

Typically, this function will be used to build Second-order Cone Programming (SOCP) problems which might be formulated in the following way:

$$\begin{array}{c}\begin{array}{ccc}{minimize}_{x\in R^n}& c^{T}x& \text{(a)}\\ \text{subject to}& l_B\le Bx\le u_B\text{,}& \text{(b)}\\ & l_x\le x\le u_x\text{,}& \text{(c)}\\ & x_{G^i}\in K^{m_i},i=1,\dots ,r\text{,}& \text{(d)}\end{array}\end{array}$$

where $K^{m_i}$ is either a quadratic cone or a rotated quadratic cone of dimension $m_i$.

handle_set_group can be called repeatedly to add, replace or delete one cone constraint at a time. Note that it is also possible to temporarily disable and enable individual cone constraints in the model by calling handle_disable() and handle_enable(), respectively. See the E04 Introduction for more details about the NAG optimization modelling suite.

See also

naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main()