Interior-point ℓ2-penalty methods for nonlinear programming with strong global convergence properties

2006 ◽  
Vol 108 (1) ◽  
pp. 1-36 ◽  
Author(s):  
L. Chen ◽  
D. Goldfarb
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Interior Point ◽  
Penalty Methods ◽  
Convergence Properties

scholarly journals A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties

2003 ◽  
Vol 14 (1) ◽  
pp. 173-199 ◽  
Author(s):  
André L. Tits ◽  
Andreas Wächter ◽  
Sasan Bakhtiari ◽  
Thomas J. Urban ◽  
Craig T. Lawrence
Keyword(s):  
Nonlinear Programming ◽  
Interior Point ◽  
Local Convergence ◽  
Interior Point Method ◽  
Point Method ◽  
Convergence Properties ◽  
Primal Dual ◽  
Global And Local

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

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