The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial...

<Para ID="Par1">We consider a class of nonsmooth convex optimization problems where the objective function is a convex differentiable function regularized by the sum of the group reproducing kernel norm and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell _1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation>-norm of the problem variables. This class of problems has many applications in...</equationsource></equationsource></inlineequation></para>

When data sets are multilevel (group nesting or repeated measures), different sources of variations must be identified. In the framework of unsupervised analyses, multilevel simultaneous component analysis (MSCA) has recently been proposed as the most satisfactory option for analyzing multilevel...