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The routine CPXgetgrad can be used, after an LP has been
solved and a basis is available, to access information useful for different
types of post-solution analysis. CPXgetgrad provides two
arrays that can be used to project the impact of making changes to optimal
variable values or objective function coefficients.
For a unit change in the value of the jth variable, the
value of the ith basic variable, sometimes referred to as the
variable basic in the ith row, changes by the amount
y[i]. Also, for a unit change of the objective function
coefficient of the ith basic variable, the reduced-cost of the
jth variable changes by the amount y[i]. The
vector y is equal to the product of the inverse of the basis
matrix and the column j of the constraint matrix. Thus,
y can be thought of as the representation of the
jth column in terms of the basis.
Example
status = CPXgetgrad (env, lp, 13, head, y);
| env | A pointer to the CPLEX environment as returned by |
| lp | A pointer to a CPLEX problem object as returned by |
| j | An integer indicating the index of the column of interest. A negative value for |
| head | An array to contain a listing of the indices of the basic variables in the order in which they appear in the basis. This listing is sometimes called the basis header. The |
| y | An array to contain the coefficients of the Example status = CPXgetgrad (env, lp, 13, head, y); |