Infeasibility certificate from an unbounded Lagrangian dual
= Infeasibility certificate from an unbounded Lagrangian dual
For a maximization problem, every <feasible point>'s finite objective is bounded above by every valid <Lagrangian relaxation> value. If a sequence of nonnegative multipliers makes those upper bounds tend to minus infinity, no <feasible point> can exist. Thus a minimization <Lagrangian dual problem> unbounded below certifies primal infeasibility. Finite dual value alone does not certify primal feasibility.