scholarly journals A Filter Algorithm with Inexact Line Search

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Meiling Liu ◽  
Xueqian Li ◽  
Qinmin Wu
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Local Convergence ◽  
Numerical Experiments ◽  
Line Search ◽  
Second Order ◽  
Lagrangian Function ◽  
Order Correction ◽  
Inexact Line Search ◽  
Mild Conditions

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

Global convergence of new modified CG method with inexact line search

2014 ◽  
Vol 16 (2) ◽  
pp. 17-26
Author(s):  
Latif S. Ivan ◽  
◽  
Mohammed J. Lajan ◽  
Keyword(s):  
Global Convergence ◽  
Line Search ◽  
Inexact Line Search

scholarly journals An Improved Line Search Filter Method for the System of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhong Jin ◽  
Yuqing Wang
Keyword(s):  
Global Convergence ◽  
Objective Function ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Line Search ◽  
Equality Constraints ◽  
Filter Method ◽  
System Of Nonlinear Equations ◽  
Search Filter

An improved line search filter algorithm for the system of nonlinear equations is presented. We divide the equations into two groups, one contains the equations that are treated as equality constraints and the square of other equations is regarded as objective function. Two groups of equations are updated at every iteration in the works by Nie (2004, 2006, and 2006), by Nie et al. (2008), and by Gu (2011), while we just update them at the iterations when it is needed indeed. As a consequence, the scale of the calculation is decreased in a certain degree. Under some suitable conditions the global convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.

Global and local convergence of a filter line search method for nonlinear programming

2007 ◽  
Vol 22 (3) ◽  
pp. 365-390 ◽  
Author(s):  
Choong Ming Chin ◽  
Abdul Halim Abdul Rashid ◽  
Khalid Mohamed Nor
Keyword(s):  
Nonlinear Programming ◽  
Local Convergence ◽  
Line Search ◽  
Search Method ◽  
Line Search Method ◽  
Global And Local

scholarly journals Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huiping Cao
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Large Scale ◽  
Line Search ◽  
Jacobian Matrix ◽  
Nonmonotone Line Search ◽  
Broyden’S Method ◽  
Large Scale Problems ◽  
Broyden's Method

Schubert’s method is an extension of Broyden’s method for solving sparse nonlinear equations, which can preserve the zero-nonzero structure defined by the sparse Jacobian matrix and can retain many good properties of Broyden’s method. In particular, Schubert’s method has been proved to be locally andq-superlinearly convergent. In this paper, we globalize Schubert’s method by using a nonmonotone line search. Under appropriate conditions, we show that the proposed algorithm converges globally and superlinearly. Some preliminary numerical experiments are presented, which demonstrate that our algorithm is effective for large-scale problems.

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