CPXXaddindconstraints and CPXaddindconstraints

Description

The routine CPXXaddindconstraints/CPXaddindconstraints adds a set of indicator constraints to the specified problem object. You can call this routine any time after a call to CPXXcreateprob/CPXcreateprob.

An indicator constraint defines a relationship between a binary variable (the indicator variable) and a linear constraint. The linear constraint can be a less-than-or-equal-to constraint, a greater-than-or-equal-to constraint, or an equality constraint. There are three types of indicator constraints:

• CPX_INDICATOR_IF: In this case, the linear constraint is enforced only if the indicator variable is not complemented and takes the value 1 (one) or if it is complemented and takes the value 0 (zero).
• CPX_INDICATOR_ONLYIF: This case is the reverse of the previous case. If the linear constraint is satisfied, then the indicator variable must take the value 1 (one) if it is not complemented or must take the value 0 (zero) if it is complemented.
• CPX_INDICATOR_IFANDONLYIF. Both of the previous cases must hold true.

In the case of CPX_INDICATOR_ONLYIF, the condition is whether the linear constraint (say, ax <= b) is satisfied or not. When it is not satisfied, then CPLEX is dealing with a strict inequality. Since strict inqualities cannot be represented as such, CPLEX handles this dichotomy as ax <= b and ax >= b + epsilon. The "only if" part of CPX_INDICATOR_IFANDONLYIF is treated similarly. CPLEX consults the linearization parameter epsilon (degree of tolerance) used in linearization when it needs to perform this transformation.

The linear portion of the indicator constraints are specified in the same style that rows-to-be-added are specified in CPXXaddrows and CPXaddrows.

Arguments

env

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

lp

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

indcnt

The number of indicator constraints. This argument specifies the length of the arrays in the arguments indvar, complemented, rhs, sense, linbeg, type, indname.

type

An array of integers that specifies the type (CPX_INDICATOR_IF, CPX_INDICATOR_ONLYIF, or CPX_INDICATOR_IFANDONLYIF) of each indicator constraint. This argument can be NULL; in that case, all entries are set to CPX_INDICATOR_IF.

indvar

The indices of the binary variables that act as the indicator variables for the indicator constraints. This argument can be NULL; in that case, all entries are set to -1. (That is, no indicator variable is set.)

complemented

An array of Boolean values that specify for each indicator variable whether the variable is complemented. This argument can be NULL; in that case, all entries are set to 0 (zero).

nzcnt

The total number of nonzero coefficients in the linear constraint part of the indicator constraints. This argument gives the length of the arrays linind and linval.

rhs

The righthand side values for the linear portion of the indicator constraints. This argument can be NULL; in that case, all entries are set to 0.0 (zero point zero).

sense

The sense values of the linear portion of the indicator constraints. Specify 'L' for <= or 'G' for >= or 'E' for ==. This argument can be NULL; in that case, all entries are set to 'E'.

linbeg

An array used with linind and linval to define the linear portion of the indicator constraints.

linind

An array used with linbeg and linval to define the linear portion of the indicator constraints.

linval

An array used with linbeg and linind to define the the linear portion of the indicator constraints. The format is similar to the format used to define the rows-to-be-added in the routine CPXXaddrows and CPXaddrows. (See also the description of rcnt, nzcnt, rmatbeg, rmatind, and rmatval in that routine).

indname

The array of the names of the constraint constraints. This argument can be NULL; in that case, the new constraints are assigned a default name if the indicator constraints already resident in the CPLEX problem object have names; otherwise, no names are associated with the new constraints.

Return

Example

   status = CPXaddindconstraints (env, lp, numind, type, indicator,
                                 complemented, nzcnt,
                                 rhs, sense, linbeg, linind, linval,
				 newindnames);