Augmented lagrangian nonlinear programming algorithm that uses SQP and trust region techniques

1995 ◽  
Vol 86 (2) ◽  
pp. 311-325 ◽  
Author(s):  
M. L. Psiaki ◽  
K. Park
Keyword(s):  
Nonlinear Programming ◽  
Augmented Lagrangian ◽  
Trust Region ◽  
Programming Algorithm

A Nonlinear Programming Algorithm for Optimizing Conventional Beamformer Shading Weights

2003 ◽  
Author(s):  
Thomas A. Wettergren ◽  
John P. Casey ◽  
Charles M. Traweek
Keyword(s):  
Nonlinear Programming ◽  
Programming Algorithm

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.

scholarly journals Using a Cable-Driven Parallel Robot with Applications in 3D Concrete Printing

2021 ◽  
Vol 11 (2) ◽  
pp. 563
Author(s):  
Tuong Phuoc Tho ◽  
Nguyen Truong Thinh
Keyword(s):  
3D Printing ◽  
Large Scale ◽  
Trust Region ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Programming Algorithm ◽  
Construction Time ◽  
Inverse Kinematic Problem ◽  
Robot Configuration ◽  
Printing Method

In construction, a large-scale 3D printing method for construction is used to build houses quickly, based on Computerized Aid Design. Currently, the construction industry is beginning to apply quite a lot of 3D printing technologies to create buildings that require a quick construction time and complex structures that classical methods cannot implement. In this paper, a Cable-Driven Parallel Robot (CDPR) is described for the 3D printing of concrete for building a house. The CDPR structures are designed to be suitable for 3D printing in a large workspace. A linear programming algorithm was used to quickly calculate the inverse kinematic problem with the force equilibrium condition for the moving platform; this method is suitable for the flexible configuration of a CDPR corresponding to the various spaces. Cable sagging was also analyzed by the Trust-Region-Dogleg algorithm to increase the accuracy of the inverse kinematic problem for controlling the robot to perform basic trajectory interpolation movements. The paper also covers the design and analysis of a concrete extruder for the 3D printing method. The analytical results are experimented with based on a prototype of the CDPR to evaluate the work ability and suitability of this design. The results show that this design is suitable for 3D printing in construction, with high precision and a stable trajectory printing. The robot configuration can be easily adjusted and calculated to suit the construction space, while maintaining rigidity as well as an adequate operating space. The actuators are compact, easy to disassemble and move, and capable of accommodating a wide variety of dimensions.

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