Specifics of hybrid mathematical programming methods applied to machine translation within contemporary linguistic

Abstract

This paper investigates hybrid mathematical optimization as a key approach to enhancing machine translation systems. By integrating continuous neural network representations with discrete decoding algorithms and expert linguistic constraints, these systems overcome the limitations of isolated statistical or neural methods. The study analyzes implementation mechanisms, such as multi-criteria quality functions and various algorithmic combination strategies, which allow for the simultaneous minimization of lexical, syntactic, and semantic losses. The findings demonstrate that hybrid models provide superior accuracy, interpretability, and adaptability, particularly in specialized domains or under conditions of data scarcity. Ultimately, the synthesis of mathematical tools and cognitive-linguistic knowledge is presented as the foundation for the next generation of human-oriented translation technologies