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DancingOwl (talk | contribs) →Lagrange multipliers: reference for definition of the Lagrangian function |
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:<math>\mathcal{X} = \left\{x\in X \vert g_1(x), \ldots, g_m(x)\leq 0\right\}.</math>
The Lagrangian function for the problem is<ref>{{cite book |first1=Brian |last1=Beavis |first2=Ian M. |last2=Dobbs |chapter=Static Optimization |title=Optimization and Stability Theory for Economic Analysis |___location=New York |publisher=Cambridge University Press |year=1990 |isbn=0-521-33605-8 |page=40 |chapter-url=https://books.google.com/books?id=L7HMACFgnXMC&pg=PA40 }}</ref>
:<math>L(x,\lambda_{0},\lambda_1, \ldots ,\lambda_{m})=\lambda_{0} f(x) + \lambda_{1} g_{1} (x)+\cdots + \lambda_{m} g_{m} (x).</math>
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