Name
Abstract | ||
|---|---|---|
Modern barrier methods for constrained optimization are sometimes portrayed conceptually as a sequence of inexact minimizations, with only a very few Newton iterations (perhaps just one) for each value of the barrier parameter. Unfortunately, this rosy image does not accurately reflect reality when the barrier parameter is reduced at a reasonable rate, as in a practical (long-step) method. Local analysis is presented indicating why a pure Newton step in a typical long-step barrier method for nonlinearly constrained optimization may be seriously infeasible, even when taken from an apparently favorable point; hence accurate calculation of the Newton direction does not guarantee an effective algorithm. The features described are illustrated numerically and connected to known theoretical results for well-behaved convex problems satisfying common assumptions such as self-concordancy. The contrasting nature of an approximate step to the desired minimizer of the barrier function is also discussed. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1137/0805001 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
INTERIOR METHOD,LOGARITHMIC BARRIER FUNCTION,PRIMAL METHOD,PRIMAL NEWTON STEP | Newton fractal,Mathematical optimization,Regular polygon,Barrier function,Barrier method,Newton's method in optimization,Local analysis,Mathematics,Constrained optimization | Journal |
Volume | Issue | ISSN |
5 | 1 | 1052-6234 |
Citations | PageRank | References |
15 | 8.21 | 5 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Margaret H. Wright | 1 | 1233 | 182.31 |