Computing the Local-Nonglobal Minimizer of a Large Scale Trust-Region Subproblem

2005 ◽  
Vol 16 (1) ◽  
pp. 263-296 ◽  
Author(s):  
Charles Fortin
Keyword(s):  
Large Scale ◽  
Trust Region ◽  
Trust Region Subproblem

scholarly journals A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Weiwei ◽  
Yang Yueting ◽  
Zhang Chenhui ◽  
Cao Mingyuan
Keyword(s):  
Large Scale ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Nonconvex Minimization ◽  
Trust Region Subproblem ◽  
Newton Equation ◽  
Limited Memory ◽  
Quasi Newton ◽  
Approximate Hessian

We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.

scholarly journals A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem

2001 ◽  
Vol 11 (3) ◽  
pp. 611-646 ◽  
Author(s):  
Marielba Rojas ◽  
Sandra A. Santos ◽  
Danny C. Sorensen
Keyword(s):  
Large Scale ◽  
Trust Region ◽  
Trust Region Subproblem ◽  
Matrix Free

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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