We consider iterative trust region algorithms for the unconstrained minimization of an objective function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$F ( \underline{x})$</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\underline{x}\in \mathcal{R}^{n}$</EquationSource> </InlineEquation>, when F is differentiable but no derivatives are available, and when each model of F is a linear or a quadratic polynomial. The...</equationsource></inlineequation></equationsource></inlineequation>