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--- title: "Duality for Feasible Problems" source: https://www.jemoka.com/posts/kbhduality_for_feasible_problems/ --- Consider feasible problems. \begin{align} \min_{x}\quad & 0 \\ \textrm{s.t.} \quad & \dots \end{align} so the optimal is either \(p^{*} = 0\) or \(p^{*} = +\infty\). And thus the Lagrange Dual Problem boils down to checking if \(d^{*} \geq 0\), if so, then the original problem is’nt feasible (since dual gives a lower bound.)