[en] In the class B(t), t>0, of all functions f(z,t)=e^-t+c₁(t)z+c₂(t)z²+... that are analytic in the unit disc U and such that 0<|f(z,t)|<1 in U, we obtain asymptotic estimates for the coefficients for small and sufficiently large t>0. We suggest an algorithm for determining those t>0 for which the canonical functions provide the local maximum of Re c_n(t) in B(t). We describe the set of functionals Lf)=Σ_k=0ⁿλ_kc_k for which the canonical functions provide the maximum of Re L(f) in B(t) for small and large values of t. The proofs are based on optimization methods for solutions of control systems of differential equations