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Aero Glass for Windows 8.1 | Apella Aero Glass for Windows 8.1 comes free. It’s a. Windows 8 and Windows 8.1, you can use this tool to bring back the Aero effect.
Aero Glass for Windows 8.1 | Apella Aero Glass for Windows 8.1 comes free. It’s a. Windows 8 and Windows 8.1, you can use this tool to bring back the Aero effect.
Aero Glass for Windows 8.1 | Apella Aero Glass for Windows 8.1 comes free. It’s a. Windows 8 and Windows 8.1, you can use this tool to bring back the Aero effect.
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Try to solve $\min_w \|w-\theta\|_2^2 \text{ subject to } w_i \ge 0 \text{ for all } i$

I would like to solve the following problem in python.
I have $\theta \in \mathbb{R}^p$ and $\mathbf{y} \in \mathbb{R}^m$ where $\mathbf{y}$ is the observed feature vectors.
I want to minimize $\|w-\theta\|_2^2$ subject to $w_i \ge 0$ for all $i$. That is, we want $w$ to lie in the convex hull of the observed feature vectors.
I would like to solve this in Python.

A:

Is there any thing special about $w$ lying on the convex hull of $\mathbf{y}$?
For that matter, for the $m$ constraints ($w_i \geq 0$) you can also use a mixed-integer (MI) problem solver (e.g. Cplex, Gurobi)

If you do want to find the minimum $\|w – \theta\|_2$ with $w_i \geq 0$ for all $i$, then you are, in a very general sense, asking for a solution $w$ to the following continuous problem:
$$ \min_{w} \|w-\theta\|_2^2 \quad \text{subject to} \quad w_i \geq 0 \quad i=1,\dots,m $$
If I understand the problem correctly you also want to find the constraint $w_i=0$ where $w_i$ is non-positive.
If you represent $w$ as a vector in $\mathbb{R}^{m+1}$ (one additional row for the unconstrained $w_0$)
$$ w=(w_0, w_1, \dots, w_m)$$
then you have a quadratic programming (QP) problem
$$ \min_{w_0} \|w-\
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