Resultados de convergencia global mejorados para el Método de Lagrangiano aumentado con función de penalidad exponencial
DOI:
https://doi.org/10.17268/sel.mat.2024.02.02Palavras-chave:
Programación no lineal, métodos Lagrangiano aumentado, función de penalización exponencial, convergencia global, condiciones de calificación, condiciones de optimalidad secuencialResumo
El propósito del presente artículo es el de mejorar los resultados de convergencia global establecidos hasta ahora, referentes al Algoritmo de Lagrangiano aumentado con función de penalidad exponencial para resolver problemas de programación no lineal con restricciones de igualdad y de desigualdad. Demostramos la convergencia global para puntos KKT bajo la condición de calificación PAKKT-regular, que resulta como una consecuencia de que puntos de acumulación generados por el algoritmo son puntos PAKKT. Este resultado de convergencia es nuevo para el Método Lagrangiano aumentado basado en la función de penalización exponencial. Una consecuencia interesante es que las estimaciones de los multiplicadores de Lagrange calculadas por el método permanecen acotados en presencia de la condición de cuasi-normalidad. Finalmente damos resultados de optimalidad y viabilidad para el caso convexo.
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