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An indefinite quadratic formulation for sparse vector optimization
Dori Peleg and Ron Meir
Signal Processing
2006.
AbstractSparsity plays an important role in many fields
of engineering. The cardinality penalty function, aka the “zero
norm”, 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 an indefinite quadratic 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. [Edit]
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