Convex Optimization: Farkas' Lemma

This lecture covers the concept of Farkas' lemma, which states that two assertions hold true if and only if the optimal value of certain linear programs is zero. The lecture delves into Lagrangian duality theory to prove this fact, using specific linear programs as examples. Through various exercises, students will explore the relationship between different linear programs and understand the conditions under which Farkas' lemma applies.