The paper presents a method for solving the optimization problem min\(\{\) cx\(|\) h(x)\(\leq 0\), g(x)\(\leq 0\}\), where \(c\in R^ n\), h a convex function and g a concave function on \(R^ n\). The algorithm is applied to a convex programming problem with complementarity type constraints and to a design centering problem with polyhedral structure.