In this paper, we discuss the following inequality constrained optimization problem (P) minf(x) subject tog(x)⩽0,g(x)=(g1(x), ...,gr(x))τ, wheref(x),gj(x)(j=1, ...,r) are locally Lipschitz functions. TheL1 exact penalty function of the problem (P) is (PC) minf(x)+cp(x) subject tox eRn, wherep(x)=max {0,g1(x), ...,gr(x)},c>0. We will discuss the relationships between (P) and (PC). In particular, we will prove that under some (mild) conditions a local minimum of (PC) is also a local minimum of (P).