Solve linear equations system with only positive coefficients in solution

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Can you advice the most efficient way to solve a system of linear equations where the solution vector has only positive coordinates?

$$A \times b = c$$ $$\forall i,\, b_i > 0$$ Of course, in most cases exact solution does not exist, so the task is to minimize the error: $$b = \arg\min \|A\times b - c\|_2$$