Surrogate-based optimisation in design spaces exceeding several tens of parameters is numerically intractable yet more and more frequent. Dimension reduction is a potent answer to this problem. However, typical dimension reduction methods seek to identify global trends over the entire design space. We propose to use a combination of Active Subspaces in subregions of the design space, where their use of the objective function’s gradients will exploit local information to discover specific trends in the objective function. Local surrogate models are then constructed in the subspaces, and recombined to form a global surrogate model, which we can then exploit for optimisation. The partitioning of the input space is done through a model based Gaussian Mixture Model clustering, where the authors assume the distribution of the joint inputs/outputs to be a mixture of Gaussians. Traditional enrichment processes rely on probability of cluster membership estimated from GMM hyperparameters. Instead, after labelling the points with GMM, we propose to train a supervised Support Vector Classifier. This strategy scales better with high-dimensional parameter spaces and yields an explicit analytical expression of the clusters’ boundaries, from which we can formulate an improved recombination strategy with overlapping between the surrogate models. The use of overlapping increases prediction accuracy at the boundaries between clusters, an improvement over recombination methods typically found in the literature. We then present a hybrid optimisation strategy, consisting of a Surrogate-Based Optimisation in the reduced space, followed by gradient descent to accelerate convergence towards the global optimum. The use of gradient information is a recurring theme in this work, as we benefit from recent improvements to adjoint computation in ONERA's CFD solver elsA. The strategy is benchmarked on well known analytical test cases, and showcases contributions to constraint management in the context of dimension reduction.