# incremental approach to solve positive least square problem

Is there any incremental (approximate) solution for the following positive least squares problem:

$$\min_x \|Ax-b\|^2\qquad \textrm{s.t.}\qquad x_i> 0,~b_1=1,~b_{i>1}=0$$

• Your problem comes under the so-called quadratic programming with linear constraints. It is a well studied problem. – dineshdileep Jan 18 '15 at 8:27
• @dineshdileep Could you please elaborate more? – Elrond Gimli Jan 18 '15 at 8:33

If you relax the constraint into $x \succeq 0$ then the problem becomes a Convex Problem.
\begin{align*} {x}^{k + 1} & = {x}^{k} + \alpha {A}^{T} \left( A x - b \right) \\ {x}^{k + 2} & = \max \left\{ {x}^{k + 1}, 0 \right\} \end{align*}