A Non-Interior Predictor-Corrector Path-Following Method for LCP

1998 ◽  
pp. 45-63 ◽  
Author(s):  
James V. Burke ◽  
Song Xu
Keyword(s):  
Path Following ◽  
Predictor Corrector

scholarly journals A predictor-corrector path-following algorithm for symmetric optimization based on Darvay's technique

2014 ◽  
Vol 24 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Path Following ◽  
Euclidean Jordan Algebra ◽  
Symmetric Cone ◽  
Interior Point Algorithm ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Symmetric Cone Optimization ◽  
Predictor Corrector ◽  
Corrector Step ◽  
Predictor Step

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is o(?rlogr?/?), where r is the rank of Euclidean Jordan algebra.

Perturbed path following predictor-corrector interior point algorithms

1999 ◽  
Vol 11 (1-4) ◽  
pp. 183-210 ◽  
Author(s):  
J. Frédéric Bonnans ◽  
Cecilia Pola ◽  
Raja Rébai
Keyword(s):  
Interior Point ◽  
Path Following ◽  
Interior Point Algorithms ◽  
Predictor Corrector

Continuation and path following

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 1-64 ◽  
Author(s):  
Eugene L. Allgower ◽  
Kurt Georg
Keyword(s):  
Eigenvalue Problems ◽  
Piecewise Linear ◽  
Path Following ◽  
Parametric Programming ◽  
Polynomial Systems ◽  
Nonlinear Eigenvalue Problems ◽  
Interior Methods ◽  
Main Ideas ◽  
New Applications ◽  
Predictor Corrector

The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed. Complexity issues and available software are also discussed.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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