Aplicaciones de los Sistemas Matemáticos en la Resolución de Problemas de Optimización en Ingeniería y Finanzas

Optimization plays a key role in engineering and finance, enabling the resolution of complex problems under specific constraints. In Latin America, its application is essential for improving resource management efficiency and decision-making in uncertain scenarios. This study aims to analyze the implementation of advanced mathematical optimization models and their impact on various sectors. The methodology is based on the development and application of optimization algorithms, algebraic models, and numerical analysis, considering case studies in power grid planning, sustainable structural design, and financial portfolio management. Methods such as linear and nonlinear optimization, dynamic programming, and advanced heuristics were employed, evaluating their effectiveness in cost reduction, increased operational efficiency, and improved project sustainability. The results show that optimization significantly contributes to technological innovation and sustainable development, although it faces challenges related to computational complexity and the need for high-quality data. It was identified that the integration of artificial intelligence and high-performance computing can enhance the applicability of these models, enabling more precise and scalable solutions. This study highlights the importance of adaptive strategies to overcome technical limitations and maximize the impact of optimization in strategic sectors, fostering its adoption in resource-limited contexts and promoting decision-making based on robust mathematical models.