Abstract Wireless communication systems play an essential role in everyday life situations and enable a wide range of location-based services to their users. The imminent adoption of 5G networks worldwide and the future establishment of next-generation wireless networks will allow various applications, such as autonomous vehicles, connected robotics, and most recently, crowd monitoring for fighting infectious diseases, such as COVID-19. In this context, radio localization techniques have become an essential tool to provide solid performance for mobile positioning systems, through increased accuracy or less computational time. With this in mind, we propose a trilateration-based approach using machine learning (ML) and sequential least-square programming (SLSQP) optimization to estimate the outdoor position of mobile terminals in cellular networks. The ML technique employed is the k -nearest neighbors ( k -NN). The optimization methods analyzed are Nelder–Mead (NM), genetic algorithms (GA), and SLSQP. Different environments (noise-free and noisy) and network scenarios (different numbers of base stations) are considered to evaluate the approaches. Numerical results indicate that the k -NN/SLSQP technique has similar accuracy compared to the k -NN/GA with eight generations. Both perform better than k -NN/NM in all scenarios and environments. When comparing computational times, our proposal is considerably more time-efficient. Aside from that, SLSQP computational time is less affected by network scenarios with more base stations in comparison with GA. That feature is significant considering the ultra-dense base station deployment forecasted for the next-generation cellular networks.