EXPERIMENTAL BEHAVIOR OF AN INTERIOR-POINT CUTTING PLANE ALGORITHM FOR CONVEX-PROGRAMMING - AN APPLICATION TO GEOMETRIC-PROGRAMMING

This paper deals with the computation of the interior point cutting plane algorithm of Goffin, Haurie and Vial, with a special application to the solution of convex differentiable programming problems. The interior point cutting plane algorithm is closely related to the classical method of Cheney and Goldstein, and Kelley, but the cuts are generated from different, more central, points in order to achieve deeper cuts and thereby accelerate convergence. The method is quite general in purpose as it can be applied to a large class of convex differentiable and nondifferentiable optimization problems. The paper focuses on the different stages of a MATLAB implementation and the overall performance of the algorithm. The test problems come from a set of convex geometric programming problems.