NAG CL Interface
e04rbc (handle_​set_​group)

1 Purpose

e04rbc 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.

2 Specification

#include <nag.h>
void  e04rbc (void *handle, const char *gtype, Integer lgroup, const Integer group[], Integer *idgroup, NagError *fail)
The function may be called by the names: e04rbc or nag_opt_handle_set_group.

3 Description

After the initialization function e04rac has been called, e04rbc may be used to edit a model by adding, replacing, or deleting a cone constraint i of dimension mi. The supported cones are quadratic cone and rotated quadratic cone, also known as second-order cones, which are defined as follows:
The cone constraint is defined by its type and a subset (group) of variables. Let index set Gi1,2,,n denote variable indices, then xGi will denote the subvector of variables xn.
For example, if mi=3 and Gi=4,1,2, then a quadratic cone constraint
xGi = x4,x1,x2 Kq3  
implies the inequality constraints
x42 x12 + x22 ,   x4 0 .  
Typically, this function will be used to build second-order cone programming (SOCP) problems which might be formulated in the following way:
minimize xn cTx   (a) subject to lBBxuB,   (b) lxxux ,   (c) xGiKmi,i=1,,r,   (d) (3)
where Kmi is either quadratic cone or rotated quadratic cone of dimension mi.
e04rbc can be called repeatedly to add, replace or delete one cone constraint at a time. See Section 4.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References


5 Arguments

1: handle void * Input
On entry: the handle to the problem. It needs to be initialized by e04rac and must not be changed before the call to e04rbc.
2: gtype const char * Input
On entry: the type of the cone constraint, case insensitive.
gtype=QUAD or Q
The group defines a quadratic cone.
gtype=RQUAD or R
The group defines a rotated quadratic cone.
Constraint: gtype=QUAD, Q, RQUAD or R.
3: lgroup Integer Input
On entry: mi, the number of the variables in the group.
If lgroup=0, gtype and group will not be referenced and may be NULL, and the constraint with ID number idgroup will be deleted from the model.
  • if gtype=QUAD or Q, lgroup=0 or lgroup2;
  • if gtype=RQUAD or R, lgroup=0 or lgroup3.
4: group[lgroup] const Integer Input
On entry: Gi, the indices of the variables in the constraint. If lgroup=0, group is not referenced and may be NULL.
Constraint: 1group[k]n, for k=0,1,,lgroup , where n is the number of decision variables in the problem. The elements must not repeat and each variable can appear in one cone at most, see Section 9.
5: idgroup Integer * Input/Output
On entry:
A new cone constraint is created.
i, the ID number of the existing constraint to be deleted or replaced.
Constraint: idgroup0.
On exit: if idgroup=0 on entry, the ID number of the new cone constraint is returned. By definition, this is the number of the cone constraints already defined plus one. Otherwise, idgroup stays unchanged.
6: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
The supplied handle does not define a valid handle to the data structure for the NAG optimization modelling suite. It has not been initialized by e04rac or it has been corrupted.
On entry, k=value, group[k-1]=value and n=value.
Constraint: 1group[k-1]n.
On entry, idgroup=value.
Constraint: idgroup0.
On entry, lgroup=value.
Constraint: lgroup0.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The problem cannot be modified in this phase any more, the solver has already been called.
On entry, idgroup=value.
The given idgroup does not match with any cone constraint already defined.
On entry, variable with index i=value has been defined in a cone in a previous call to this function.
Constraint: each variable may be defined in one cone constraint at most.
On entry, group[i-1]=group[j-1]=value for i=value and j=value.
Constraint: elements in group cannot repeat.
On entry, gtype=value and lgroup=value.
Constraint: if gtype=QUAD or Q, lgroup=0 or lgroup2.
On entry, gtype=value and lgroup=value.
Constraint: if gtype=RQUAD or R, lgroup=0 or lgroup3.
On entry, gtype=value.
Constraint: gtype=QUAD, Q, RQUAD or R.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04rbc is not threaded in any implementation.

9 Further Comments

Overlapping of cones is not supported, which means each variable may be defined in one cone at most. However by adding auxiliary variables, you can achieve the same effect. For example, if xaKm1 and xaKm2, you can add one more variable xb=xa and set xaKm1, xbKm2.

10 Example

This example solves the following SOCP problem
minimize 10.0x1 + 20.0x2 + x3  
subject to the bounds
-2.0 x1 2.0 -2.0 x2 2.0  
the general linear constraints
-0.1x1 - 0.1x2 + x3 1.5 1.0 -0.06x1 + x2 + x3  
and the cone constraint
x3,x1,x2 K q 3 .  
The optimal solution (to five significant figures) is
and the objective function value is -19.518.

10.1 Program Text

Program Text (e04rbce.c)

10.2 Program Data

Program Data (e04rbce.d)

10.3 Program Results

Program Results (e04rbce.r)