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

Juan Peypouquet ()
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Juan Peypouquet: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 1, No 8, 123-138

Abstract: 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.

Keywords: Convex optimization; Hierarchical minimization; Exterior penalization; Non-autonomous gradient-like systems (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-011-9936-x

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