Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the principle of minimal sensitivity can be unambiguously implemented at order ${\ensuremath{\partial}}^{2}$ of the derivative expansion. This approach allows us to select optimized cutoff functions and to improve the accuracy of the critical exponents $\ensuremath{\nu}$ and $\ensuremath{\eta}.$ The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.