Line Search Filter Methods for Nonlinear Programming: Local Convergence

2005 ◽  
Vol 16 (1) ◽  
pp. 32-48 ◽  
Author(s):  
Andreas Wächter ◽  
Lorenz T. Biegler
Keyword(s):  
Nonlinear Programming ◽  
Local Convergence ◽  
Line Search ◽  
Search Filter ◽  
Filter Methods

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.

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 A Class of Inexact Secant Algorithms with Line Search Filter Method for Nonlinear Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhujun Wang ◽  
Li Cai
Keyword(s):  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Filter Method ◽  
Inexact Line Search ◽  
Search Filter ◽  
Filter Methods ◽  
Line Search Method ◽  
Secant Methods ◽  
Scale Optimization

We propose a class of inexact secant methods in association with the line search filter technique for solving nonlinear equality constrained optimization. Compared with other filter methods that combine the line search method applied in most large-scale optimization problems, the inexact line search filter algorithm is more flexible and realizable. In this paper, we focus on the analysis of the local superlinear convergence rate of the algorithms, while their global convergence properties can be obtained by making an analogy with our previous work. These methods have been implemented in a Matlab code, and detailed numerical results indicate that the proposed algorithms are efficient for 43 problems from the CUTEr test set.

scholarly journals Comparison of Filter Line Search Algorithms in the Primal-Dual Barrier Approach for Nonlinear Programming

2009 ◽  
Author(s):  
M. Fernanda P. Costa ◽  
Edite M. G. P. Fernandes ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Nonlinear Programming ◽  
Line Search ◽  
Search Algorithms ◽  
Primal Dual

A penalty method for nonlinear programming

2019 ◽  
Vol 53 (1) ◽  
pp. 29-38
Author(s):  
Larbi Bachir Cherif ◽  
Bachir Merikhi
Keyword(s):  
Nonlinear Programming ◽  
Convex Programming ◽  
Penalty Method ◽  
Line Search ◽  
Penalty Methods ◽  
Descent Direction ◽  
Type Method ◽  
Numerical Tests ◽  
Line Searches ◽  
Majorant Function

This paper presents a variant of logarithmic penalty methods for nonlinear convex programming. If the descent direction is obtained through a classical Newton-type method, the line search is done on a majorant function. Numerical tests show the efficiency of this approach versus classical line searches.

Global convergence of slanting filter methods for nonlinear programming

2008 ◽  
Vol 200 (2) ◽  
pp. 486-500 ◽  
Author(s):  
Elizabeth W. Karas ◽  
Ana P. Oening ◽  
Ademir A. Ribeiro
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Filter Methods
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