Minimizing pseudoconvex functions on convex compact sets

An algorithm is presented which minimizes continuously differentiable pseudoconvex 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 constraint 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.