problem.loadproblem

Purpose

Load an optimization problem, possibly with quadratic objective and/or constraints, and integer variables.

Synopsis

problem.loadproblem(probname, qrtypes, rhs, range, obj, mstart, mnel, mrwind, dmatval, dlb, dub, mqcol1, mqcol2, dqe, qcrows, qcnquads, qcmqcol1, qcmqcol2, qcdqval, qgtype, mgcols, dlim, qstype, msstart, mscols, dref, colnames, rownames)

Arguments

probname

A string of up to 200 characters containing the problem name.

qrtype

Character array 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

Array 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

Array containing the range values for range rows. Values for all other rows will be ignored. May be None 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

Array containing the objective function coefficients.

mstart

Array containing the offsets in the mrwind and dmatval arrays of the start of the elements for each column. This array is of length equal to the number ncol of added variables or, if mnel is None, ncol+1. If mnel is None 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.

mnel

Array containing the number of nonzero elements in each column. May be None 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 None if not required.

mrwind

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 None, mstart[ncol].

dmatval

Array containing the nonzero element values; length as for mrwind.

dlb

Array containing the lower bounds on the columns. Use -xpress.infinity to represent a lower bound of minus infinity.

dub

Array containing the upper bounds on the columns. Use xpress.infinity to represent an upper bound of plus infinity.

mqc1

(optional) Array with the first variable in each quadratic term.

mqc2

(optional) Array with the second variable in each quadratic term.

dqe

(optional) Array with the quadratic coefficients.

qcrows

(optional) Integer 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

(optional) Array containing the number of nonzeros in each quadratic constraint matrix.

qcmqcol1

(optional) Array with a number of elements equal to 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

(optional) Array containing the second index for the quadratic constraint matrices.

qcdqval

(optional) Array containing the coefficients for the quadratic constraint matrices.

qgtype

Character array containing the entity types:

B	binary variables;
I	integer variables;
P	partial integer variables;
S	semi-continuous variables;
R	semi-continuous integer variables.

mgcols

(optional) Array containing the variables of the global entities.

dlim

(optional) Array containing the integer limits for the partial integer variables and lower bounds for semi-continuous and semi-continuous integer variables (any entries in the positions corresponding to binary and integer variables will be ignored). May be None if not required.

qstype

(optional) Character array of length equal to the number of sets specified, problem.attributes.nsets, and specifies the set types:

1	SOS1 type sets;
2	SOS2 type sets.

May be None if not required.

msstart

(optional) Array containing the offsets in the mscols and dref arrays indicating the start of the sets. This array is of length nsets+1, the last member containing the offset where set nsets+1 would start. May be None if not required.

mscols

(optional) Array of length msstart[nsets]-1 containing the columns in each set. May be None if not required.

dref

(optional) Array of length msstart[nsets]-1 containing the reference row entries for each member of the sets. May be None if not required.

colname

(optional) Array of containing the column names for all variables added.

rowname

(optional) Array of containing the row names for all constraints added.

Further information

1. The objective function is of the form c^Tx+ 1/2 x^TQx 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. If indices are specified, both row and column indices are from 0 to rows-1 and 0 to cols-1 respectively.

4. Semi-continuous lower bounds are taken from the dlim array. If this is None then they are given a default value of 1.0. If a semi-continuous variable has a positive lower bound then this will be used as the semi-continuous lower bound and the lower bound on the variable will be set to zero.

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