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XPRSloadqcqp, XPRSloadqcqp64

XPRSloadqcqp, XPRSloadqcqp64


Purpose
Used to load a quadratic problem with quadratic side constraints into the Optimizer data structure. Such a problem may have quadratic terms in its objective function as well as in its constraints.
Synopsis
int XPRS_CC XPRSloadqcqp(XPRSprob prob, const char * probname, int ncol, int nrow, const char qrtypes[], const double rhs[], const double range[], const double obj[], const int mstart[], const int mnel[], const int mrwind[], const double dmatval[], const double dlb[], const double dub[], int nqtr, const int mqcol1[], const int mqcol2[], const double dqe[], int qmn, const int qcrows[], const int qcnquads[], const int qcmqcol1[], const int qcmqcol2[], const double qcdqval[]);

int XPRS_CC XPRSloadqcqp64(XPRSprob prob, const char * probname, int ncol, int nrow, const char qrtypes[], const double rhs[], const double range[], const double obj[], const XPRSint64 mstart[], const int mnel[], const int mrwind[], const double dmatval[], const double dlb[], const double dub[], XPRSint64 nqtr, const int mqcol1[], const int mqcol2[], const double dqe[], int qmn, const int qcrows[], const XPRSint64 qcnquads[], const int qcmqcol1[], const int qcmqcol2[], const double qcdqval[]);
Arguments
prob 
The current problem.
probname 
A string of up to MAXPROBNAMELENGTH characters containing a name for the problem.
ncol 
Number of structural columns in the matrix.
nrow 
Number of rows in the matrix (not including the objective row). Objective coefficients must be supplied in the obj array, and the objective function should not be included in any of the other arrays.
qrtype 
Character array of length nrow containing the row types:
indicates a <= constraint (use this one for quadratic constraints as well);
indicates an = constraint;
indicates a >= constraint;
indicates a range constraint;
indicates a nonbinding constraint.
rhs 
Double array of length nrow containing the right hand side coefficients of the rows. The right hand side value for a range row gives the upper bound on the row.
range 
Double array of length nrow containing the range values for range rows. Values for all other rows will be ignored. May be NULL if there are no ranged constraints. The lower bound on a range row is the right hand side value minus the range value. The sign of the range value is ignored - the absolute value is used in all cases.
obj 
Double array of length ncol containing the objective function coefficients.
mstart 
Integer array containing the offsets in the mrwind and dmatval arrays of the start of the elements for each column. This array is of length ncol or, if mnel is NULL, length ncol+1. If mnel is NULL the extra entry of mstart, mstart[ncol], contains the position in the mrwind and dmatval arrays at which an extra column would start, if it were present. In C, this value is also the length of the mrwind and dmatval arrays.
mnel 
Integer array of length ncol containing the number of nonzero elements in each column. May be NULL if all elements are contiguous and mstart[ncol] contains the offset where the elements for column ncol+1 would start. This array is not required if the non-zero coefficients in the mrwind and dmatval arrays are continuous, and the mstart array has ncol+1 entries as described above. It may be NULL if not required.
mrwind 
Integer array containing the row indices for the nonzero elements in each column. If the indices are input contiguously, with the columns in ascending order, the length of the mrwind is mstart[ncol-1]+mnel[ncol-1] or, if mnel is NULL, mstart[ncol].
dmatval 
Double array containing the nonzero element values; length as for mrwind.
dlb 
Double array of length ncol containing the lower bounds on the columns. Use XPRS_MINUSINFINITY to represent a lower bound of minus infinity.
dub 
Double array of length ncol containing the upper bounds on the columns. Use XPRS_PLUSINFINITY to represent an upper bound of plus infinity.
nqtr 
Number of quadratic terms.
mqc1 
Integer array of size nqtr containing the column index of the first variable in each quadratic term.
mqc2 
Integer array of size nqtr containing the column index of the second variable in each quadratic term.
dqe 
Double array of size nqtr containing the quadratic coefficients.
qmn 
Number of rows containing quadratic matrices.
qcrows 
Integer array of size qmn, containing the indices of rows with quadratic matrices in them. Note that the rows are expected to be defined in qrtype as type L.
qcnquads 
Integer array of size qmn, containing the number of nonzeros in each quadratic constraint matrix.
qcmqcol1 
Integer array of size nqcelem, where nqcelem equals the sum of the elements in qcnquads (i.e. the total number of quadratic matrix elements in all the constraints). It contains the first column indices of the quadratic matrices. Indices for the first matrix are listed from 0 to qcnquads[0]-1, for the second matrix from qcnquads[0] to qcnquads[0]+ qcnquads[1]-1, etc.
qcmqcol2 
Integer array of size nqcelem, containing the second index for the quadratic constraint matrices.
qcdqval 
Integer array of size nqcelem, containing the coefficients for the quadratic constraint matrices.
Related controls
Integer
Number of extra columns to be allowed for.
Number of extra matrix elements to be allowed for.
Number of extra global entities to be allowed for.
Number of extra elements to allow for in presolve.
Number of extra qcqp elements to be allowed for.
Number of extra qcqp matrices to be allowed for.
Number of extra rows to be allowed for.
Status for nonbinding rows.
Type of scaling.

Double
Tolerance on matrix elements.

Example
To load the following problem presented in LP format:
minimize [ x^2 ]
s.t.
4 x + y <= 4
x + y + [z^2] <= 5
 [ x^2 + 2 x*y + y^2 + 4 y*z + z^2 ] <= 10
x + 2 y >= 8
 [ 3 y^2 ] <= 20
end
the following code may be used:
{
    int ncols = 3;
    int nrows = 5;
    char rowtypes[] = {'L','L','L','G','L'};
    double rhs[] = {4,5,10,8,20};
    double range[] = {0,0,0,0,0};
    double obj[] = {0,0,0,0,0};
    int mstart[] = {0,3,6,6};
    int* mnel = NULL;
    int mrind[] = {0,1,3,0,1,3};
    double dmatval[] = {4,1,1,1,1,2};
    double lb[] = {0,0,0};
    double ub[] = {XPRS_PLUSINFINITY,XPRS_PLUSINFINITY,
    XPRS_PLUSINFINITY};

    int nqtr = 1;
    int mqc1[] = {0};
    int mqc2[] = {0};
    double dqe[] = {1};

    int qmn = 3;
    int qcrows[] = {1,2,4};
    int qcnquads[] = {1,5,1};
    int qcmcol1[] = {2,0,0,1,1,2,1};
    int qcmcol2[] = {2,0,1,1,2,2,1};
    // ! to have 2xy define 1xy (1yx will be assumed to be implicitly present)
    double qcdqval[] = {1,9,1,8,2,7,3};
}

XPRSloadqcqp(xprob,"qcqp",ncols,nrows,rowtypes,rhs,range,obj,mstart,
mnel,mrind,dmatval,lb,ub,nqtr,mqc1,mqc2,dqe,qmn,qcrows,qcnquads,
qcmcol1,qcmcol2,qcdqval);

}

Further information
1. The objective function is of the form cTx+ 0.5 xTQx where Q is positive semi-definite for minimization problems and negative semi-definite for maximization problems. If this is not the case the optimization algorithms may converge to a local optimum or may not converge at all. Note that only the upper or lower triangular part of the Q matrix is specified.
2. All Q matrices in the constraints must be positive semi-definite. Note that only the upper or lower triangular part of the Q matrix is specified for constraints as well.
3. The row and column indices follow the usual C convention of going from 0 to nrow-1 and 0 to ncol-1 respectively.
4. The double constants XPRS_PLUSINFINITY and XPRS_MINUSINFINITY are defined in the Optimizer library header file.
Related topics

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