We study the optimization of evaporative cooling in trapped bosonic atoms on the basis of quantum kinetic theory of a Bose gas. The optimized cooling trajectory for ^87Rb atoms indicates that the acceleration of evaporative cooling around the transition point of Bose-Einstein condensation is very effective against loss of trapped atoms caused by three-body recombination. The number of condensed atoms is largely enhanced by the optimization, more than two orders of magnitude in our present

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... ation using relevant experimental parameters, as compared with the typical value given by the conventional evaporative cooling where the frequency of radio-frequency magnetic field is swept exponentially. In addition to this optimized cooling, it is also shown that highly efficient evaporative cooling can be achieved by an initial exponential and then a rapid linear sweep of frequency.