The steady advances of computational methods make model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line. In addition, the resulting model may poorly represent the plant when there is structural mismatch between the two. The iterative optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, principally in the form of constraint values and gradients. However, the experimental cost (i.e. the number of experiments required) to estimate these gradients increases linearly with the number of process inputs, which tends to make the method intractable for processes with many inputs. This paper presents a new algorithm, called Directional Modier Adaptation, that overcomes this limitation by only estimating the plant gradients in certain privileged directions. It is proven that plant optimality with respect to these privileged directions can be guaranteed upon convergence. A novel, statistically optimal, gradient estimation technique is developed. The algorithm is illustrated through the simulation of a realistic airborne wind-energy system, a promising renewable energy technology that harnesses wind energy using large kites. It is shown that Directional Modifier Adaptation can optimize in real time the path followed by the dynamically flying kite.