i'd like to know if there is an analytical method to solve the following optimisation problem : $\forall i=1,..,n$ find $\omega_i^{}$ and $\alpha_i^{}$ such that:

$\dfrac{1}{n} \displaystyle \sum_{i=1}^{n} \Big(\omega_i^{} X_i - \alpha_i^{} Y_i \Big)= M$

where $\displaystyle\sum_{i=1}^{n} \omega_i^{}=\displaystyle\sum_{i=1}^{n} \alpha_i^{}=n$ and $X_i,Y_i \in \mathbb{R}_{+}$ and $M\in \mathbb{R}$

  • $\begingroup$ Why do you think this is nonlinear optimisation? The degree of the decision variables is one in each term. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Apr 14 at 21:22
  • $\begingroup$ Could you clarify what needs to be optimized? That is, what needs to maximized/minimized? $\endgroup$ – AzJ Apr 14 at 22:18
  • $\begingroup$ the aim is to find the weight $\omega_i$ and $\alpha_i$ that minimize the distance between the two means through an analytical method. $\endgroup$ – user41037 Apr 14 at 22:54

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