The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. In this article, we propose an outer approximation algorithm for maximizing a function $h(x) = \varphi(f(x))$ over the efficient set $X_E$ of the bi-criteria convex programming problem $ {\rm Vmin} \{f(x)=(f_1(x), f_2(x))^T | x \in X \}$, where $\varphi$ is an increasing function on $f(X)$. The convergence of the algorithm is established. To illustrate the new algorithm, we apply it to the solution of the sample problem. Preliminary computational results with the proposed algorithm are reported.
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