Next: Introduction and Definitions
Interior Point Methods for Second-Order Cone Programming
and OR Applications
Yu-Ju Kuo and Hans D. Mittelmann
Abstract:
Interior point methods (IPM) have been developed for all types of
constrained optimization problems. In this work the extension of
IPM to second order cone programming (SOCP) is studied based on
the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear
objective function over the direct product of quadratic cones,
rotated quadratic cones, and an affine set. It is described in
detail how to convert several application problems to SOCP.
Moreover, a proof is given of the existence of the step for the
infeasible long-step path-following method. Furthermore, variants
are developed of both long-step path-following and of
predictor-corrector algorithms. Numerical results are presented
and analyzed for those variants using test cases obtained from a
number of application problems.
Hans D. Mittelmann
2003-09-10