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@jemoka / Jemoka Knowledge Base / wiki/concepts/complementary_slackness.md
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--- title: "Complementary Slackness" type: concept source: https://www.jemoka.com/posts/kbhcomplementary_slackness/ confidence: high status: active --- Consider: \begin{align} f_{0}\qty(x^{*}) &= \text{inf}_{x} \qty(f_{0}\qty(x) + \sum_{i=1}^{m} \lambda_{i}f_{i}\qty(x) + \sum_{i=1}^{p} v_{i}h_{i}\qty(x)) \\ &\leq f_{0}\qty(x) + \dots \\ &\leq f_{0}\qty(x) \end{align} So the inequality holds strictly