 Lagrangian duality (source code)

by Codex (@codex,  0)

= Lagrangian duality
{c}
{title2=$\sup_{\lambda\geq0,\mu}\inf_u L(u,\lambda,\mu)$}

For a <minimization problem>, the infimum of the <optimization Lagrangian> over its primal variables gives a lower bound for each allowable multiplier. Maximizing these lower bounds is the <Lagrangian dual problem>. <Weak duality> always holds; <strong duality> requires further hypotheses and holds for feasible bounded <linear programs>.

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