A Generalized Reduced Gradient Algorithm for Large-scale Trajectory Optimization Problems

1995 ◽  
pp. 117-132 ◽  
Author(s):  
Kathryn E. Brenan ◽  
Wayne P. Hallman
Keyword(s):  
Trajectory Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Algorithm

A New Method to Solve the Kinematic Problems of Parallel Robots Using Generalized Reduced Gradient Algorithm

2016 ◽  
Vol 28 (3) ◽  
pp. 404-417 ◽  
Author(s):  
Thanh Trung Trang ◽  
◽  
Wei Guang Li ◽  
Thanh Long Pham ◽  
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
New Method ◽  
Gradient Algorithm ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Algorithm

[abstFig src='/00280003/17.jpg' width=""300"" text='Stewart Gough robot and the equivalent substitutional configuration' ] This paper proposes a new method of solving the kinematic problems for parallel robots. The paper content aims to solve nonlinear optimization problems with constraints rather than to directly solve high-order nonlinear systems of equations. The nonlinear optimization problems shall be efficiently solved by applying the Generalized Reduced Gradient algorithm and appropriate downgrade techniques. This new method can be able to find exact kinematic solutions by assigning constraints onto the parameters. The procedure can be done without filtering control results from mathematical solution, from which the control time of manipulators can be reduced. The numerical simulation results in this paper shall prove that the method can be applied to solve kinematic problems for a variety of parallel robots regardless of its structures and degree of freedom (DOF). There are several advantages of the proposed method including its simplicity leading to a shorter computing time as well as achieving high accuracy, high reliability, and quick convergence in final results. Hence, the applicability of this method in solving kinematic problems for parallel manipulators is remarkably high.

scholarly journals Tolerance Design of Robot Parameters Using Generalized Reduced Gradient Algorithm

2017 ◽  
Vol 5 (2) ◽  
pp. 96-105
Author(s):  
Trang Thanh Trung ◽  
◽  
Wei Guang Li ◽  
Pham Thanh Long ◽  
◽  
...  
Keyword(s):  
Gradient Algorithm ◽  
Tolerance Design ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Algorithm

scholarly journals Design optimization of the box section of the single-girder bridge crane by generalized reduced gradient algorithm

2015 ◽  
Vol 21 (4) ◽  
pp. 79-86 ◽  
Author(s):  
Goran Pavlović ◽  
Aleksandar Stepanović ◽  
Jelena Vidaković ◽  
Mile Savković ◽  
Nebojša Zdravković
Keyword(s):  
Design Optimization ◽  
Gradient Algorithm ◽  
Bridge Crane ◽  
Box Section ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Girder Bridge ◽  
Reduced Gradient Algorithm

A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equation

2021 ◽  
pp. 2150053
Author(s):  
Jie Guo ◽  
Zhong Wan
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Large Scale Optimization ◽  
Newton Equation ◽  
Numerical Performance ◽  
Scale Optimization ◽  
Quasi Newton

A new spectral three-term conjugate gradient algorithm in virtue of the Quasi-Newton equation is developed for solving large-scale unconstrained optimization problems. It is proved that the search directions in this algorithm always satisfy a sufficiently descent condition independent of any line search. Global convergence is established for general objective functions if the strong Wolfe line search is used. Numerical experiments are employed to show its high numerical performance in solving large-scale optimization problems. Particularly, the developed algorithm is implemented to solve the 100 benchmark test problems from CUTE with different sizes from 1000 to 10,000, in comparison with some similar ones in the literature. The numerical results demonstrate that our algorithm outperforms the state-of-the-art ones in terms of less CPU time, less number of iteration or less number of function evaluation.

Optimal Design of Semisubmersible’s Form Based on Systems Analysis

1984 ◽  
Vol 106 (4) ◽  
pp. 524-530 ◽  
Author(s):  
S. Akagi ◽  
R. Yokoyama ◽  
K. Ito
Keyword(s):  
Optimal Design ◽  
Computer Aided Design ◽  
Optimization Problem ◽  
Design Method ◽  
Gradient Algorithm ◽  
Interpretive Structural Modeling ◽  
Reduced Gradient ◽  
Optimal Design Method ◽  
Generalized Reduced Gradient ◽  
Aided Design

With the objective of developing a computer-aided design method to seek the optimal semisubmersible’s form, hierarchical relationships among many design objectives and conditions are investigated first based on the interpretive structural modeling method. Then, an optimal design method is formulated as a nonlinear multiobjective optimization problem by adopting three mutually conflicting design objectives. A set of Pareto optimal solutions is derived numerically by adopting the generalized reduced gradient algorithm, and it is ascertained that the designer can determine the optimal form more rationally by investigating the trade-off relationships among design objectives.

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