Function estimation in inverse heat transfer problems
Résumé
This lecture presents some commonly-used numerical algorithms devoted to optimization, that is maximizing or, more often minimizing a given function of several variables. The goal is function estimation. At rst, some general mathematical tools are presented. Some gradient-free optimization algorithms are presented and then some gradient-type methods are pointed out with pros and cons for each method. The gradient of the function to be minimized is presented according to three distinct methods: nite di erence, forward di erentiation and the use of the additional adjoint-state problem. The last part presents some practical studies where some tricks are given, along with some numerical results.
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