For a given constant lambda>0 and a bounded Lipschitz domain D subset of R-n(n >= 2), we establish that almost-minimizers of the functional J(v;D)=(D)integral(m)& sum;(i=1)|del vi(x)|(p)+lambda chi{|v|>0}(x) dx, 1<p<infinity, where v=(v(1),<middle dot><middle dot><middle dot>,v(m)),and m is an element of N , and , exhibit optimal Lipschitz continuity in compact sets of D. Furthermore, assuming p >= 2 and employing a distinctly different methodology, we tackle the issue of boundary Lipschitz regularity for <bold>v</bold>. This approach simultaneously yields an alternative proof for the optimal local Lipschitz regularity for the interior case.