Regularized Gradient Algorithm for Convex Problems with Constraints

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3650 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3650 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3650 archive 351 disk0/00/00/36/33 2016-01-15 02:01:51 2021-08-27 17:14:12 2016-01-15 02:01:51 monograph show 2 Aubin J.-P. 7347 Regularized Gradient Algorithm for Convex Problems with Constraints pub iis_met prog_ado Nesterov has proved the convergence of the discrete subgradient algorithm for minimizing convex finite functions bounded from below. When the objective function is a lower semicontinuous convex extended function (which happens when one minimizes problems with constraints), the subgradient algorithm no longer makes sense since we do not know whether the iterations belong to the domain of the objective function. Hence the idea is to approximate the objective function by its Moreau-Yosida approximation, which is differentiable, and to use the gradient algorithm applied to this approximation. We prove the convergence when both the steps of the algorithm converge to infinity and the Moreau-Yosida parameter converges to 0. 1992-08 published WP-92-066 WP-92-066 10 1134 public working_paper IIASA, Laxenburg, Austria 8 FALSE info:eu-repo/semantics/book