The authors study the constrained nonlinear programming problem min\(\{\) f(x)\(|\) g(x)\(\leq 0\), \(h(x)=0\}\), where g: \(R^ n\to R^ m\), h: \(R^ n\to R^ l\). Instead of solving the constrained problem directly, they study the nonsmooth exact penalty function \(\phi (x,N)=f(x)+N\| g^+(x)\), \(h(x)\|\), where \(g^+(x)=g^+_ 1(x),...,g^+_ m(x))^ and\) \(\| \cdot \|\) is the Euclidean norm in the corresponding space \(g^+_ i(x)=\max \{0,g_ i(x)\}\). They propose a quadratic programming and inexact line search based algorithm to minimize \(\phi\) (x,N). Under certain conditions, they prove that every unconditional local minimum of \(\phi\) (x,N) is a solution of the constrained problem and that every limit point of the sequence generated by their algorithm is a Kuhn-Tucker point of the constrained problem.