We consider the following problem, which occurs in the software being developed by the author for minimizing a general function F(x), when derivatives of F(x) are not available and when there are linear constraints on the vector of variables x. Let M(x) be a quadratic approximation to F(x), and let X be the set of vectors x that satisfy the constraints. Having chosen a trust region centre c in X and a trust region radius r, we seek a relatively small value of M(x) subject to x in X and ||x-c|| .leq. r. Active sets are employed, which give an unconstrained trust region problem in fewer variables for each active set. Only low accuracy is required. Examples show that major difficulties arise if one attempts to calculate a global solution instead of a local solution to the trust region problem with linear constraints.