CPXXaddlazyconstraints and CPXaddlazyconstraints

Description

The routine CPXXaddlazyconstraints/CPXaddlazyconstraints adds constraints to the list of constraints that should be added to the LP subproblem of a MIP optimization if they are violated. CPLEX handles addition of the constraints and makes sure that all integer solutions satisfy all the constraints. The constraints are added to those specified in prior calls to CPXXaddlazyconstraints/CPXaddlazyconstraints.

Lazy constraints are constraints not specified in the constraint matrix of the MIP problem, but that must be not be violated in a solution. Using lazy constraints makes sense when there are a large number of constraints that must be satisfied at a solution, but are unlikely to be violated if they are left out.

The CPLEX parameter that controls primal and dual reduction type (CPXPARAM_Preprocessing_Reduce) should be set to CPX_PREREDUCE_NOPRIMALORDUAL(0) or to CPX_PREREDUCE_PRIMALONLY(1) in order to turn off dual reductions.

Use CPXXfreelazyconstraints/CPXfreelazyconstraints to clear the list of lazy constraints.

The arguments of CPXXaddlazyconstraints/CPXaddlazyconstraints are similar to those of CPXXaddrows/CPXaddrows, with the exception that new columns may not be specified, so there are no rcnt and rowname arguments. Furthermore, unlike CPXXaddrows/CPXaddrows, CPXXaddlazyconstraints/CPXaddlazyconstraints does not accept a NULL pointer for the array of righthand side values or senses. Nor does it accept ranged rows as lazy constraints. Acceptable values of the array sense appear in the table.

Arguments

env

A pointer to the CPLEX environment as returned by CPXXopenCPLEX/CPXopenCPLEX.

lp

A pointer to a CPLEX problem object as returned by CPXXcreateprob/CPXcreateprob.

rcnt

An integer that specifies the number of new lazy constraints to be added.

nzcnt

An integer that specifies the number of nonzero constraint coefficients to be added to the constraint matrix. This specifies the length of the arrays rmatind and rmatval.

rhs

An array of length rcnt containing the righthand side (RHS) term for each lazy constraint to be added to the CPLEX problem object.

sense

An array of length rcnt containing the sense of each lazy constraint to be added to the CPLEX problem object. Possible values of this argument appear in the table.

rmatbeg

An array used with rmatind and rmatval to define the lazy constraints to be added.

rmatind

An array used with rmatbeg and rmatval to define the lazy constraints to be added.

rmatval

An array used with rmatbeg and rmatind to define the lazy constraints to be added. The format is similar to the format used to describe the constraint matrix in the routine CPXXcopylp/CPXcopylp (see description of matbeg, matcnt, matind, and matval in that routine), but the nonzero coefficients are grouped by row instead of column in the array rmatval. The nonzero elements of every lazy constraint must be stored in sequential locations in this array from position rmatbeg[i] to rmatbeg[i+1]-1 (or from rmatbeg[i] to nzcnt-1 if i=rcnt-1). Each entry, rmatind[i], specifies the column index of the corresponding coefficient, rmatval[i]. UnlikeCPXcopylp, all rows must be contiguous, and rmatbeg[0] must be 0 (zero).

rowname

An array containing pointers to character strings that represent the names of the lazy constraints. Can be NULL, in which case the new lazy constraints are assigned default names if the lazy constraints already resident in the CPLEX problem object have names; otherwise, no names are associated with the lazy constraints. If row names are passed to CPXXaddlazyconstraints/CPXaddlazyconstraints but existing lazy constraints have no names assigned, default names are created for them.

Return

Example

 status = CPXaddlazyconstraints (env, lp, cnt, nzcnt, rhs, sense,
                                 beg, ind, val, NULL);