On using Quadratic Interpolation of the Determinant Function to Estimate the Step-Length in a Predictor-Corrector Variant for Semidefinite Programming

2009 ◽  
Author(s):  
A. Teixeira ◽  
F. Bastos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Semidefinite Programming ◽  
Step Length ◽  
Quadratic Interpolation ◽  
Predictor Corrector ◽  
Determinant Function

scholarly journals A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
C. C. Cui ◽  
S. X. Xie ◽  
X. C. Huang ◽  
J. K. Liu ◽  
Y. M. Chen
Keyword(s):  
Accurate Determination ◽  
Step Length ◽  
Computational Accuracy ◽  
Time Step ◽  
Aeroelastic System ◽  
Precise Integration ◽  
Runge Kutta Method ◽  
Hysteresis Nonlinearity ◽  
Major Procedure ◽  
Predictor Corrector

We propose an accurate approach, based on the precise integration method, to solve the aeroelastic system of an airfoil with a pitch hysteresis. A major procedure for achieving high precision is to design a predictor-corrector algorithm. This algorithm enables accurate determination of switching points resulting from the hysteresis. Numerical examples show that the results obtained by the presented method are in excellent agreement with exact solutions. In addition, the high accuracy can be maintained as the time step increases in a reasonable range. It is also found that the Runge-Kutta method may sometimes provide quite different and even fallacious results, though the step length is much less than that adopted in the presented method. With such high computational accuracy, the presented method could be applicable in dynamical systems with hysteresis nonlinearities.

scholarly journals An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
M. Y. Waziri ◽  
Z. A. Majid
Keyword(s):  
Nonlinear Equations ◽  
Line Search ◽  
Step Length ◽  
Search Strategies ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Convergence Results ◽  
Overall Performance ◽  
Predictor Corrector ◽  
Matrix Free

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.

scholarly journals PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING

2009 ◽  
Vol 79 (3) ◽  
pp. 367-376
Author(s):  
CAIYING WU ◽  
GUOQING CHEN
Keyword(s):  
Global Convergence ◽  
Semidefinite Programming ◽  
Optimality Conditions ◽  
Newton Method ◽  
Superlinear Convergence ◽  
Smoothing Newton Method ◽  
Equivalent Transformation ◽  
Newton Algorithm ◽  
Smoothing Methods ◽  
Predictor Corrector

AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

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