Most of modern multi-objective machine learning methods are based on evolutionary optimization algorithms. They are known to be global convergent, however, usually deliver nondeterministic results. In this work we propose the deterministic global solution to a multi-objective problem of supervised learning with the methodology of nonlinear programming. As the result, the proposed multi-objective algorithm performs a global search of Pareto-optimal hypotheses in the space of RBF networks, determining their weights and basis functions. In combination with the Akaike and Bayesian information criteria, the algorithm demonstrates a high generalization efficiency on several synthetic and real-world benchmark problems.