scholarly journals Research on trust-region algorithms for nonlinear programming. Progress report, January 1, 1991--December 31, 1991

1991 ◽  
Author(s):  
J.E. Dennis ◽  
R.A. Tapia
Keyword(s):  
Nonlinear Programming ◽  
Trust Region ◽  
Progress Report ◽  
Trust Region Algorithms

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.

Global convergence of trust-region algorithms for convex constrained minimization without derivatives

2013 ◽  
Vol 220 ◽  
pp. 324-330 ◽  
Author(s):  
P.D. Conejo ◽  
E.W. Karas ◽  
L.G. Pedroso ◽  
A.A. Ribeiro ◽  
M. Sachine
Keyword(s):  
Global Convergence ◽  
Trust Region ◽  
Constrained Minimization ◽  
Trust Region Algorithms

Trust region algorithms for the nonlinear least distance problem

1995 ◽  
Vol 9 (1) ◽  
pp. 171-179 ◽  
Author(s):  
H. -P. Helfrich ◽  
D. Zwick
Keyword(s):  
Trust Region ◽  
Trust Region Algorithms ◽  
Distance Problem
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