Lq quasi-norm ($\Vert x{\Vert }_q=({\sum }_i|x_i{|}^q{)}^{1/q},0<q<1$)

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.