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</math><br> | </math><br> | ||
where <math>\mathcal{L}(w, \alpha, \beta) = f(w) + \sum \alpha_i g_i(w) + \sum \beta_i h_i(w)</math> is called the lagrangian.<br> | where <math>\mathcal{L}(w, \alpha, \beta) = f(w) + \sum \alpha_i g_i(w) + \sum \beta_i h_i(w)</math> is called the lagrangian.<br> | ||
Since <math>\min | Since <math>\max \min \leq \max \min</math>,<br> | ||
we have:<br> | we have:<br> | ||
<math> | <math> | ||
\max_{\alpha, \beta \mid \alpha \geq 0}\min_{w} \mathcal{L}(w, \alpha, \beta) \leq \min_{w}\max_{\alpha, \beta \mid \alpha \geq 0} \mathcal{L}(w, \alpha, \beta) | |||
</math><br> | </math><br> | ||
The left term is called the dual problem.<br> | The left term is called the dual problem.<br> |