Gradients and optimization with constraints in economics and social sciencesAbstract
Despite their widespread use in advanced analytical and numerical techniques, gradient field methods are often underrepresented in the foundational training of economists and social scientists. As machine learning and sophisticated analytical and numerical approaches gain traction, the importance of gradient methods in optimization processes becomes increasingly apparent. This oversight in academic and practical toolsets is suboptimal. This paper aims to address this gap by introducing gradient field methods both intuitively and rigorously, situating them within the context of problems commonly encountered by economists and social scientists, with a particular focus on equality constrained optimization.
Keywords: Minimization with constraints; Lagrange multipliers; Gradient fields algorithms.
Resumen
A pesar de su uso generalizado en técnicas analíticas y numéricas avanzadas, los métodos de campo de gradientes suelen estar subrepresentados en la formación básica de economistas y científicos sociales. A medida que el aprendizaje automático y los enfoques analíticos y numéricos sofisticados ganan terreno, la importancia de los métodos de gradiente en los procesos de optimización se vuelve cada vez más evidente. Esta falta en las herramientas académicas y prácticas es subóptima. Este artículo tiene como objetivo abordar esta brecha introduciendo los métodos de campo de gradientes tanto de manera intuitiva como rigurosa, situándolos en el contexto de problemas comúnmente encontrados por economistas y científicos sociales, con un enfoque particular en la optimización con restricciones de igualdad.
Palabras clave: Minimización con restricciones; Multiplicadores de Lagrange; Algoritmos con campos de gradientes.
Mathematics Subject Classification: Primary 97M40; Secondary 49-01, 49K05, 49K10, 49K21, 97G70, 97H60, 97I99, 97M70, 97P99.
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Publication Dates
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Date of issue
Jul-Dec 2024
History
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Received
07 Nov 2023 -
Accepted
16 May 2024
