  We use the optimized perturbation theory, or linear delta expansion, to
evaluate the critical exponents in the critical 3d O(N) invariant scalar field
model. Regarding the implementation procedure, this is the first successful
attempt to use the method in this type of evaluation. We present and discuss
all the associated subtleties producing a prescription which can, in principle,
be extended to higher orders in a consistent way. Numerically, our approach,
taken at the lowest nontrivial order (second order) in the delta expansion
produces a modest improvement in comparison to mean field values for the
anomalous dimension eta and correlation length nu critical exponents. However,
it nevertheless points to the right direction of the values obtained with other
methods, like the epsilon-expansion. We discuss the possibilities of improving
over our lowest order results and on the convergence to the known values when
extending the method to higher orders.
