Many real-time optimization schemes maximize process performance by performing a model-based optimization. However, due to plant-model mismatch, the model-based solution is often suboptimal. In modifier adaptation, measurements are used to correct the model in such a way that the first-order necessary conditions of optimality are satisfied for the plant. However, performing experiments to obtain measurements can be costly. This paper uses a sensitivity analysis that allows making only partial corrections to the model, thereby relying on fewer experiments. Furthermore, this sensitivity analysis is of global nature, which ensures that the corrections are sufficient in the presence of large parametric uncertainties. However, since the corrections are still only locally valid, this paper proposes to control the update step length via a trust-region technique. The resulting algorithm is illustrated via the simulation of an energy-harvesting kite.