A proximal method with separable Bregman distances for quasiconvex minimization over the nonnegative orthant |
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Authors: | Sissy da S Souza PR Oliveira JX da Cruz Neto A Soubeyran |
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Institution: | 1. PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil;2. PESC/COPPE – Programa de Engenharia de Sistemas e Computa?ão Cidade Universitária, Centro de Tecnologia, Bloco H, Sala 319 C.P. 68511, 21941-972 Rio de Janeiro – RJ, Brazil;3. Federal University of Piauí, Teresina, Brazil;4. GREQAM, Université d’Aix-Marseille II, France |
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Abstract: | We present an interior proximal method with Bregman distance, for solving the minimization problem with quasiconvex objective function under nonnegative constraints. The Bregman function is considered separable and zone coercive, and the zone is the interior of the positive orthant. Under the assumption that the solution set is nonempty and the objective function is continuously differentiable, we establish the well definedness of the sequence generated by our algorithm and obtain two important convergence results, and show in the main one that the sequence converges to a solution point of the problem when the regularization parameters go to zero. |
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Keywords: | Interior point methods Proximal methods Bregman distances Quasiconvex programming |
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