[Math] Solving box-constrained least-squares

Question

I have a linear least squares problem with linear constraints:

$$\min_x \| A x – b \|^2 \quad\text{subject to}\quad k_1 \leq x_i \leq k_2$$

Should quadratic programming be used here? If so, what would the formulation be?

Answer 1

What should be used may depend on what software you are using. Maple has a command LSSolve in its Optimization package to handle least-squares problems, including linearly-constrained ones. It uses an active-set method.