In this paper, we propose an optimal criterion for unconstrained optimization problems, which involves the transition from Cartesian coordinate system to the polar one. With this approach, each term in the Taylor series of objective function has an order of smallness and specifies a set of proportionality coefficients (PCs). Moreover, these sets are located in the variables space of original problem. Any such set consists of unity vectors multiplied by PC of an infinitely small quantity in the direction of this vector. We show that PC function has an analytical expression in the form of a linear combination of harmonics depending on polar direction angles. Logarithmic algorithm is used for finding the PCs of any infinitesimal function (IF) with first, second, etc., order of smallness. We give examples for expanding of IF with two and three variables, for which graphs of PCs up to the third order of smallness are plotted. We propose an optimal criterion, in which PCs curves are used instead of gradients, Hessians and tensors.