Farkas Lemma Certificates

Farkas' Lemma provides a powerful tool in linear algebra and convex optimization. It states that exactly one of two possibilities is true for a given matrix A and vector b: either the system Ax = b has a non-negative solution (x ≥ 0), or there exists a vector ysuch that A^Ty ≥ 0 and b^Ty < 0. This separating vector yserves as a certificate of infeasibility.

Experiment

1. Select the Wedge cone from the Cone control.
2. Select the Above wedge target from the Target control.
3. Observe that the feasibility result displays Infeasible.
4. Notice the separating certificate vector y appear in the visualization and results table.

Explore this experiment directly at https://riano.app/module/farkas-lemma-certificates.