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Abstract
En 中文
Sparsity plays an important role in many fields of engineering. The cardinality penalty function, often used as a measure of sparsity, is neither continuous nor differentiable and therefore smooth optimization algorithms cannot be applied directly. In this paper we present a continuous yet non-differentiable sparsity function which constitutes a tight lower bound on the cardinality function. The novelty of this approach is that we cast the problem of minimizing the new sparsity function as a problem with a bilinear objective function. We present a numerical comparison to other sparsity encouraging penalty functions for several applications. Additionally, we apply the techniques developed to minimize an objective function with a truncated hinge loss function. We present highly competitive results for all of the applications. (c) 2007 Elsevier B.V. All rights reserved.
Keywords:
sparsity
indefinite quadratic programming
regression
total variation
pattern classification
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