A modified PRP-type conjugate gradient projection algorithm for solving large-scale monotone nonlinear equations with convex constraint

2022 ◽  
pp. 114035
Author(s):  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed ◽  
Abubakar Sani Halilu
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Convex Constraint ◽  
Gradient Projection Algorithm

scholarly journals A New Conjugate Gradient Projection Method for Convex Constrained Nonlinear Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Pengjie Liu ◽  
Jinbao Jian ◽  
Xianzhen Jiang
Keyword(s):  
Nonlinear Equations ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Sparse Signals ◽  
Convex Constraints ◽  
Step Size ◽  
Constrained Nonlinear Equations

The conjugate gradient projection method is one of the most effective methods for solving large-scale monotone nonlinear equations with convex constraints. In this paper, a new conjugate parameter is designed to generate the search direction, and an adaptive line search strategy is improved to yield the step size, and then, a new conjugate gradient projection method is proposed for large-scale monotone nonlinear equations with convex constraints. Under mild conditions, the proposed method is proved to be globally convergent. A large number of numerical experiments for the presented method and its comparisons are executed, which indicates that the presented method is very promising. Finally, the proposed method is applied to deal with the recovery of sparse signals.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

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