Next: Bibliography
Up: Interior Point Methods for
Previous: PredictorCorrector Algorithms
Throughout this study, we discuss secondorder
cone programming theoretically as well as practically. Both the
longstep pathfollowing and predictorcorrector algorithms are
studied. Existence of the step length is shown for the
longstep method. Furthermore, a specific algorithm for choosing
the centering parameter and the size of the neighborhood
is developed and tested successfully on our test cases.
Next, several variants of predictorcorrector algorithms are also
compared. We analyze the numerical behavior of the linear and
quadratic combinations of predictor and corrector directions. The
idea of inexact Newton's method and of repeating the predictor
direction one more time are also integrated into the algorithm.
According to our numerical results, the inexact method for SOCP
can be expected to behave similarly as in LP. Overall, Algorithm
4.4 using the normal equations works best for both full and sparse
cases. The linear constraints in Example 5 lead to a full matrix.
The inexact method works competitively in every case except
Example 5.
Figure 2:
The condition number of the coefficient matrix for full linear system and normal equations
Figure 1:
Comparison of from Algorithm 4.3, H2,H3,H4

Next: Bibliography
Up: Interior Point Methods for
Previous: PredictorCorrector Algorithms
Hans D. Mittelmann
20030910