High energy focused ion (proton) micro- and nanoprobes are intensively integrated as powerful analytical tools for different scientific and technological goals. Requirements for beam characteristics of similar focusing systems are extremely rigid. The value of demagnification for micro- and nanoprobes is the main optimality criteria, and as desirable value are in the range from 50 to 100 or even more. In the paper, we reconsider the basic properties of first order focusing systems from an optimal viewpoint. The matrix formalism allows us to formulate a nonlinear programming problem for all parameters of guiding elements. For this purpose there are used computer algebra methods and tools as the first step, and then some combination of special numerical methods. As a starting point for nanoprobe we consider so called "russian quadruplet". On the next steps, we also investigate other types of nanoprobes. Some graphical and tabular data for nanoprobe parameters are cited as an example.