Nonlinear Renormalization Group Flow and Approximate Solutions

We propose a self-consistent renormalization group prescription for the scalar field theory. The formalism coincides with the local potential approximation in the sharp-cutoff limit but differs from the smooth cutoff. We explore the dependence of the critical exponent $\nu$ on the smoothness parameter and the field of expansion. We use an optimization scheme based on the minimum sensitivity principle to ensure the most rapid convergence of $\nu$ with the polynomial truncation level.