Lq quasi-norm
= Lq quasi-norm
{c}
{title2=$\|x\|_q=(\sum_i|x_i|^q)^{1/q},\quad0<q<1$}
The displayed quantity is homogeneous and separates zero, but generally violates the <triangle inequality>. Its $q$th power is subadditive because $(a+b)^q\le a^q+b^q$ for nonnegative $a,b$. Minimizing it is equivalent to minimizing its $q$th power. On finite <vectors> it is a standard nonconvex sparsity penalty.