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The IMSL_LINLSQ function solves a linear least-squares problem with linear constraints.

The IMSL_LINLSQ function solves linear least-squares problems with linear constraints. These are systems of least-squares equations of the form

Ax ≅ b

subject to

bl ≤ Cx ≤ bu

xl ≤ x ≤ xu

Here A is the coefficient matrix of the least-squares equations, b is the right-hand side, and C is the coefficient matrix of the constraints. The vectors bl, bu, xl and xu are the lower and upper bounds on the constraints and the variables, respectively. The system is solved by defining dependent variables y ≡ Cx and then solving the leastsquares system with the lower and upper bounds on x and y. The equation Cx − y = 0 is a set of equality constraints. These constraints are realized by heavy weighting, i.e., a penalty method, Hanson (1986, pp. 826-834).

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