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Coupling the Gradient Method with a General Exterior Penalization Scheme for Convex Minimization

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Abstract

In this paper, we propose and analyze an algorithm that couples the gradient method with a general exterior penalization scheme for constrained or hierarchical minimization of convex functions in Hilbert spaces. We prove that a proper but simple choice of the step sizes and penalization parameters guarantees the convergence of the algorithm to solutions for the optimization problem. We also establish robustness and stability results that account for numerical approximation errors, discuss implementation issues and provide examples in finite and infinite dimension.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile

    Juan Peypouquet

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  1. Juan Peypouquet
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Correspondence to Juan Peypouquet.

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Communicated by Jean-Pierre Crouzeix.

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Peypouquet, J. Coupling the Gradient Method with a General Exterior Penalization Scheme for Convex Minimization. J Optim Theory Appl 153, 123–138 (2012). https://doi.org/10.1007/s10957-011-9936-x

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  • DOI: https://doi.org/10.1007/s10957-011-9936-x

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