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Duality in convex optimization for the hyperbolic augmented Lagrangian

Lennin Mallma Ramirez,Nelson Maculan,Adilson Elias Xavier,Vinicius Layter Xavier

Boletín de la Sociedad Matemática Mexicana（2024）

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Abstract
We guarantee the strong duality and the existence of a saddle point of the hyperbolic augmented Lagrangian function (HALF) in convex optimization. To guarantee these results, we assume a set of convexity hypothesis and the Slater condition. Finally, we computationally illustrate our theoretical results obtained in this work.
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Key words
Hyperbolic augmented Lagrangian,Nonlinear programming,Constrained convex optimization,Saddle point,Duality,90C30,90C25,90C46,65K05
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