Initially conceived in financial engineering, advanced risk functions, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), play an important role in robust optimization problems of engineering interest. The focus is here on techniques for increasing the computational efficiency of robust optimization processes based on risk functions, whose computation is computationally demanding. In previous works, we illustrated an intrusive approach based on gradient computation and another non-intrusive approach based on Gaussian processes. Here, we analyze the performance of a mixed approach, where both the gradient information, calculated intrusively, and the approximation methodology based on Gaussian processes are used simultaneously. The new mixed approximation technique is compared and discussed in terms of efficiency and easiness of implementation differences compared to the intrusive and non-intrusive ones.