- 2019 Elsevier Ltd A derivative-free optimization framework UNIPOPT is developed to solve multi-dimensional box-constrained black-box problems. The method is based on projecting the objective function onto a univariate space, which leads to a point-to-set map. The lower envelope of the map contains the global minimum. A sensitivity theorem is employed to predict the points on the lower envelope and a trust-region based algorithm is used to correct the predictions. A model-based algorithm is used to optimize the univariate lower envelope such that its minimum corresponds to that of the original problem. We provide theoretical results related to the prediction and correction steps and prove the convergence of the overall algorithm. UNIPOPT is applied to an extensive suite of test problems comprising of both convex nonsmooth and nonconvex smooth black-box problems, and its performance is compared to the existing model-based approaches. The algorithm is able to locate global solutions for more test problems compared to the other solvers.