A class of collinear scaling algorithms for bound-constrained optimization: Derivation and computational results

A family of algorithms for the approximate solution of the bound-constrained minimization problem is described. These algorithms employ the standard barrier method, with the inner iteration based on trust region methods. Local models are conic functions rather than the usual quadratic functions, and are required to match first and second derivatives of the barrier function at the current iterate. The various members of the family are distinguished by the choice of a vector-valued parameter, which is the zero vector in the degenerate case that quadratic local models are used. Computational results are used to compare the efficiency of various members of the family on a selection of test functions.