Métodos de primeira ordem acelerados
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2022-08-18
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Universidade Federal de Goiás
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The analysis of the efficiency of algorithms to solve optimization problems is fundamental for the improvement and design of algorithms with better computational performances. Such efficiency can be measured, for example, by the “speed” in which the sequence generated by the algorithm converges to a solution of the problem at hand. From the work of Nesterov and Nemirovski in the 80's, the efficiency of an algorithm was also considered through its iteration complexity, that is, the number of iterations necessary to obtain an "approximate solution" for the problem.
In this work, we will analyze the iteration complexity of the algorithms: Iterative Shrinkage-Thresholding (ISTA), Fast Iterative Shrinkage-Thresholding (FISTA) and an accelerated Forward-Backward Nesterov type method. This study will be be carried out from a theoretical and computational point of view.
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RIBEIRO, D. N. Métodos de primeira ordem acelerados. 2022. 70 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.