Abstract
In this work we propose a derivative-free trust-region algorithm for unconstrained optimization. The algorithm is based on the ideas of Powell (Comput Optim Appl 53:527–555, 2012). We turn his general ideas into a step-form algorithm that avoids unnecessary reductions of the trust-region radius. The results related to the global convergence of the algorithm are presented in detail. We prove that, under reasonable hypotheses, any accumulation point of the sequence generated by the algorithm is stationary.
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