An efficient algorithm is derived for solving the quantile regression problem combined with a group sparsity promoting penalty. The group sparsity of the regression parameters is achieved by using a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell _{1,\infty }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>∞</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>-norm penalty (or constraint) on the regression...</equationsource></equationsource></inlineequation>