There are examples of linear programming (LP) problems where both the primal and dual problems are infeasible. For example, \begin{equation} \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} &&0\cdot x\leq -1 \end{aligned} \end{equation} On the other hand, there are examples of linear programming problems where the primal is infeasible and the dual is unbounded. For example, \begin{equation} \begin{aligned} &\min_x && x \\ &\ \ \text{s.t.} && x\geq 1 \\ & && x\leq 0 \\ \end{aligned} \end{equation} I am wondering: is there any geometric interpretation of this phenomenon? Is there some geometric difference between those infeasible LPs with infeasible duals and those infeasible LPs with unbounded duals?
Geometric Interpretation of Simultaneous Primal and Dual LP Infeasibility
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optimization
convex-optimization
linear-programming
duality-theorems