A method for convex curve approximation

In this paper, a new sandwich method is introduced to approximate a convex curve in R². This method requires only function evaluation and the solution of a number of scalar optimization problems. A quadratic convergence property of the method is established, that is, the total number of optimization problems solved is bounded by a constant multiple of the square root of the inverse of the given error. An application to approximation of the efficient frontier of a bi-criteria convex quadratic network program is given.