LpReducedCost
LpReducedCost(lp)
Computes the reduced cost -- how far a coefficient in the objective function can be increased (in a minimization program) or decreased (in a maximization program) before the objective function changes.
When a decision variable has a non-zero value in the optimal solution, any change in the objective function coefficient changes the objective value, so for those decision variables the answer will be zero. But for decision variables that are zero, the coefficient can change until that variable eventually enters the basis. This amount is known as the reduced cost (or dual value) of the variables and is returned by this function.
The reduced cost can only be computed for continuous optimization problems. The reduced cost does not exist for integer or mixed-integer optimizations.
The reduced cost for a continuous LP (from LpDefine) should always be available (emphasizing again that a continous LP has no integer variables). Likewise, it should always be available for a QP (from QpDefine) when all constraints are linear and the objective is quadratic.
For quadratically-constrained problems, the reduced cost is not available when the "SOCP Barrier" or "MOSEK" engines are used, but is generally available when other solver engines are used for the solution (provided all decision variables are continuous).
For smooth NLPs, most solver engines (except for the "Evolutionary" and "OptQuest" engines) will compute the reduced cost. The OptQuest and Evoluationary engines never provide reduced cost values.
Notes
The shadow price is also known as a dual value, but is the dual value of a constraint, while the reduced cost is the dual value of the variable.
Enable comment auto-refresher