Delta-rational chord: Difference between revisions

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and turning the objective function into a sum of univariate objective functions
and turning the objective function into a sum of univariate objective functions


<math> \displaystyle{ \sum_{l_i=1}^n \Bigg( \beta_i r_{l_i} - \beta_i - \sum_{{l_i}=1}^i \delta_{i,l_i} \Bigg)^2. } </math>
<math> \displaystyle{ \sum_{k_i=1}^{n_i} \Bigg( \beta_i r_{k_i} - \beta_i - \sum_{{l_i}=1}^i \delta_{i,l_i} \Bigg)^2. } </math>


The Hessian of the resulting objective function is positive-definite, thus the global optimum can be found by setting all individual partial derivatives to zero.
The Hessian of the resulting objective function is positive-definite, thus the global optimum can be found by setting all individual partial derivatives to zero.