At the floor
w = floor. If the lower dual is positive, the model is pressing downward.
Reference 0008
Bound Dual Cheat Sheet
How to read lower-bound and upper-bound slack, duals, and portfolio meaning.
Bound Pair
floor <= w <= cap lower slack = w - floor upper slack = cap - w
Dual Pair
lower dual > 0 -> optimizer wants w below the floor upper dual > 0 -> optimizer wants w above the cap lower slack > 0 -> lower dual should be 0 upper slack > 0 -> upper dual should be 0
Long-Only Portfolio
floor = 0 lower slack = w lower dual > 0 -> optimizer would prefer a negative or smaller weight upper dual > 0 -> optimizer would prefer a larger weight
CVXPY Pattern
constraints = [
w >= floor, # lower bounds
w <= cap, # upper bounds
cp.sum(w) == 1,
]
lower_duals = constraints[0].dual_value
upper_duals = constraints[1].dual_value
At the cap
w = cap. If the upper dual is positive, the model is pressing upward.
Inside bounds
floor < w < cap. Both bound duals should be zero, up to solver tolerance.
Constraint order
Read duals from the constraint object you created. Index names are only meaningful if you preserve the order.
Use this page with Lesson 0008, Lesson 0007, and Reference 0006.