XPRSloadqp, XPRSloadqp64

Purpose

Used to load a quadratic problem into the Optimizer data structure. Such a problem may have quadratic terms in its objective function, although not in its constraints.

Topic areas

Problem Input, Quadratic

Synopsis

int XPRS_CC XPRSloadqp(XPRSprob prob, const char *probname, int ncols, int nrows, const char rowtype[], const double rhs[], const double rng[], const double objcoef[], const int start[], const int collen[], const int rowind[], const double rowcoef[], const double lb[], const double ub[], int nobjqcoefs, const int objqcol1[], const int objqcol2[], const double objqcoef[]);

int XPRS_CC XPRSloadqp64(XPRSprob prob, const char *probname, int ncols, int nrows, const char rowtype[], const double rhs[], const double rng[], const double objcoef[], const XPRSint64 start[], const int collen[], const int rowind[], const double rowcoef[], const double lb[], const double ub[], XPRSint64 nobjqcoefs, const int objqcol1[], const int objqcol2[], const double objqcoef[]);

Arguments

prob

The current problem.

probname

A string of up to MAXPROBNAMELENGTH characters containing a names for the problem.

ncols

Number of structural columns in the matrix.

nrows

Number of rows in the matrix (not including the objective row). Objective coefficients must be supplied in the objcoef array, and the objective function should not be included in any of the other arrays.

rowtype

Character array of length nrows containing the row types:

L	indicates a ≤ constraint;
E	indicates an = constraint;
G	indicates a ≥ constraint;
R	indicates a range constraint;
N	indicates a nonbinding constraint.

rhs

Double array of length nrows 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.

rng

Double array of length nrows 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.

objcoef

Double array of length ncols containing the objective function coefficients. This can be NULL to set all objective coefficients to 0 (zero).

start

Integer array containing the offsets in the rowind and rowcoef arrays of the start of the elements for each column. This array is of length ncols or, if collen is NULL, length ncols+1. If collen is NULL the extra entry of start, start[ncols], contains the position in the rowind and rowcoef arrays at which an extra column would start, if it were present. In C, this value is also the length of the rowind and rowcoef arrays.

collen

Integer array of length ncols containing the number of nonzero elements in each column. May be NULL if all elements are contiguous and start[ncols] contains the offset where the elements for column ncols+1 would start. This array is not required if the non-zero coefficients in the rowind and rowcoef arrays are continuous, and the start array has ncols+1 entries as described above. It may be NULL if not required.

rowind

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 rowind is start[ncols-1]+collen[ncols-1] or, if collen is NULL, start[ncols].

rowcoef

Double array containing the nonzero element values; length as for rowind.

Double array of length ncols containing the lower bounds on the columns. Use XPRS_MINUSINFINITY to represent a lower bound of minus infinity. If this is NULL then all lower bounds are 0 (zero).

Double array of length ncols containing the upper bounds on the columns. Use XPRS_PLUSINFINITY to represent an upper bound of plus infinity. It this is NULL then all upper bounds are infinite.

nobjqcoefs

Number of quadratic terms.

objqcol1

Integer array of size nobjqcoefs containing the column index of the first variable in each quadratic term.

objqcol2

Integer array of size nobjqcoefs containing the column index of the second variable in each quadratic term.

objqcoef

Double array of size nobjqcoefs containing the quadratic coefficients.

Related controls

Integer

EXTRACOLS	Number of extra columns to be allowed for.
EXTRAELEMS	Number of extra matrix elements to be allowed for.
EXTRAROWS	Number of extra rows to be allowed for.
KEEPNROWS	Status for nonbinding rows.
SCALING	Type of scaling.

Double

MATRIXTOL

Tolerance on matrix elements.

Example

Minimize -6x ₁ + 2x ₁ ² - 2x ₁x ₂ + 2x ₂ ² subject to x ₁ + x ₂ ≤ 1.9:

int nrows = 1, ncols = 2, nquad = 3;
int start[] = {0, 1, 2};
int rowind[] = {0, 0};
double rowcoef[] = {1, 1};
double rhs[] = {1.9};
char rowtype[] = {'L'};
double lbound[] = {0, 0};
double ubound[] = {XPRS_PLUSINFINITY,XPRS_PLUSINFINITY};

double objcoef[] = {-6, 0};
int objqcol1[] = {0, 0, 1};
int objqcol2[] = {0, 1, 1};
double dquad[] = {4, -2, 4};

double *primal, *dual;

primal = malloc(ncols*sizeof(double));
dual = malloc(nrows*sizeof(double));
...
XPRSloadqp(prob, "example", ncols, nrows, rowtype, rhs,
           NULL, objcoef, start, NULL, rowind, rowcoef,
           lbound, ubound, nquad, objqcol1, objqcol2, dquad)

Further information

1. The objective function is of the form c'x+ 0.5 x'Qx. Note that only the upper or lower triangular part of the Q matrix is specified.

2. The row and column indices follow the usual C convention of going from 0 to nrows-1 and 0 to ncols-1 respectively.

3. The double constants XPRS_PLUSINFINITY and XPRS_MINUSINFINITY are defined in the Optimizer library header file.

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XPRSloadqp, XPRSloadqp64