# Tagged Questions

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### Are “constrained linear least squares” and “quadratic programming” the same thing?

A Quadratic Programming problem is to minimize: $f(\mathbf{x}) = \tfrac{1}{2} \mathbf{x}^T Q\mathbf{x} + \mathbf{c}^T \mathbf{x}$ subject to $A\mathbf{x} \leq \mathbf b$; $C\mathbf{x} = \mathbf d$; ...
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### Homogeneous non-negative least-squares

I would like to least-squares-"solve" a set of linear equations ($\underset{\mathbf{x}}{\mathrm{argmin}}\; \|\mathbf{Ax-b}\|_2$). In my case, $\mathbf{b=0}$, e.g. the system is homogeneous. I also ...
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### Is a given point P outside a given bounding box, in Ax < b form

Given a point $x$ and a bounding box $B$ - let's say we have the unit normals $N_i$ of the sides (pointing inwards) and one point on each side $P_i$ - we can check if $x$ is inside $B$ as follows: ...
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### Solving multiple $L_1$ penalties with quadratic programming

Starting from a simple $L_1$ penalization: $$min_x \frac{1}{2}||y-x||^2_2 + \lambda||Dx||_1$$ We can solve this with quadratic programming via the dual problem: ...