期刊
OPTIMIZATION LETTERS
卷 13, 期 4, 页码 645-655出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s11590-018-1325-z
关键词
Convex optimization; Non-smooth optimization; Proximal gradient method; Active-set identification; Active-set complexity
资金
- Natural Sciences and Engineering Research Council of Canada (NSERC) [355571-2013, 2015-06068]
- Cette recherche a ete financee par le Conseil de recherches en sciences naturelles et en genie du Canada (CRSNG) [355571-2013, 2015-06068]
Proximal gradient methods have been found to be highly effective for solving minimization problems with non-negative constraints or 1-regularization. Under suitable nondegeneracy conditions, it is known that these algorithms identify the optimal sparsity pattern for these types of problems in a finite number of iterations. However, it is not known how many iterations this may take. We introduce the notion of the active-set complexity, which in these cases is the number of iterations before an algorithm is guaranteed to have identified the final sparsity pattern. We further give a bound on the active-set complexity of proximal gradient methods in the common case of minimizing the sum of a strongly-convex smooth function and a separable convex non-smooth function.
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