Interior Point Algorithms for Second Order Cone Problems with Applications
Abstract
Interior point methods (IPM) have been
developed explosively 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. Further, 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.
