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Optimization without derivatives finds numerous and increasing applications in the industry and in computational sciences. In part this is because of the growing sophistication of computer hardware and mathematical algorithms and software, which allows expensive simulations and opens new possibilities for optimization. On the other hand, we deal more frequently with binary codes (for which the source is unavailable or owned) and legacy codes (written in the past and no longer maintained). Thus, in many circumstances, the alternatives of Derivative-Free Optimization (DFO) cannot be applied: (i) derivatives are unavailable (e.g., absence of adjoint codes); (ii) the application of automatic differentiation is too complex or impossible; (iii) even when derivatives are available, the contamination by noise and the need to search for global minimizers make them useless.
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