An algorithm is presented which minimizes continuously differentiable pseudo-convex functions on convex compact sets which are characterized by their support functions. If the function can be minimized exactly on affine sets in a finite number of operations and the constraints set is a polytope, the algorithm has finite convergence. Numerical results are reported which illustrate the performance of the algorithm when applied to a specific search direction problem. The algorithm differs from existing algorithms in that it has proven convergence when applied to any convex compact set, and not just polytopal sets.