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Derivative-free optimization involves the methods used to minimize an expensive objective function when its derivatives are not available. We present here a trust-region algorithm based on Radial Basis Functions (RBFs). The main originality of our approach is the use of RBFs to build the trust-region models and our management of the interpolation points based on Newton fundamental polynomials. Moreover the complexity of our method is very attractive. We have tested the algorithm against thedoi:10.2316/journal.205.2009.1.205-4634 fatcat:neci7asnkrcevi4dai7vbi3bve