# Find minimizer of mean values

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 $$M\in \mathbb{R}$$

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