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|Type:||Artigo de periódico|
|Title:||On perturbed steepest descent methods with inexact line search for bilevel convex optimization|
De Pierro, AR
|Abstract:||We use a general framework for solving convex constrained optimization problems introduced in an earlier work to obtain algorithms for problems with a constraint set defined as the set of minimizers of a given function. Also, the algorithms allow the objective function to be decomposed as a sum of other convex functions that can be treated separately. We prove that the general algorithm converges to the optimum of the objective function over the set of minima of a convex Lipschitz-differentiable function chosen previously. When using orthogonal projections onto the convex constraints, we retrieve a Cimmino-like algorithm that converges to the optimum over the set of weighted least squares solutions. Furthermore, we show an important application of our approach to compressed sensing and inverse problems.|
|Editor:||Taylor & Francis Ltd|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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