Data and performance profiles applying an adaptive truncation criterion, within linesearch-based truncated Newton methods, in large scale nonconvex optimization

Caliciotti, Andrea; Fasano, Giovanni; Nash, Stephen G.; Roma, Massimo

doi:10.1016/j.dib.2018.01.012

Cited by 9 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, some scholars have improved the truncation criterion of Newton's method, which avoids "over-solving" of the Newton equation as much as possible. The representative method is the heuristic adaptive truncation criterion proposed by [27,28].…”

Section: Newton's Methodsmentioning

confidence: 99%

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

et al. 2019

View full text Add to dashboard Cite

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

show abstract

Section: Newton's Methodsmentioning

confidence: 99%

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

et al. 2019

View full text Add to dashboard Cite

show abstract

“…We remark that within the Truncated Newton methods, the importance of an efficient truncation criterion for the inner iterations was pointed out in [8,9,22]. More recently, an adaptive truncation rule, in order to enhance the residual-based criterion, was proposed in [3,4].…”

Section: End Domentioning

confidence: 96%

Issues on the use of a modified Bunch and Kaufman decomposition for large scale Newton’s equation

et al. 2020

Self Cite

View full text Add to dashboard Cite

In this work, we deal with Truncated Newton methods for solving large scale (possibly nonconvex) unconstrained optimization problems. In particular, we consider the use of a modified Bunch and Kaufman factorization for solving the Newton equation, at each (outer) iteration of the method. The Bunch and Kaufman factorization of a tridiagonal matrix is an effective and stable matrix decomposition, which is well exploited in the widely adopted SYMMBK (Bunch and Kaufman in Math Comput 31:163–179, 1977; Chandra in Conjugate gradient methods for partial differential equations, vol 129, 1978; Conn et al. in Trust-region methods. MPS-SIAM series on optimization, Society for Industrial Mathematics, Philadelphia, 2000; HSL, A collection of Fortran codes for large scale scientific computation, http://www.hsl.rl.ac.uk/; Marcia in Appl Numer Math 58:449–458, 2008) routine. It can be used to provide conjugate directions, both in the case of $$1\times 1$$ 1 × 1 and $$2\times 2$$ 2 × 2 pivoting steps. The main drawback is that the resulting solution of Newton’s equation might not be gradient–related, in the case the objective function is nonconvex. Here we first focus on some theoretical properties, in order to ensure that at each iteration of the Truncated Newton method, the search direction obtained by using an adapted Bunch and Kaufman factorization is gradient–related. This allows to perform a standard Armijo-type linesearch procedure, using a bounded descent direction. Furthermore, the results of an extended numerical experience using large scale CUTEst problems is reported, showing the reliability and the efficiency of the proposed approach, both on convex and nonconvex problems.

show abstract

“…Specification refers to a system with a static structure and invariable behaviour, or a system with a variable structure at a certain time instant that both can be efficiently solved by using advanced optimization techniques proposed in [52,53]. To specify a particular system, instances of the relevant concepts appearing in the general system model should be concretised.…”

Section: Specification Of a Particular Robot Control Systemmentioning

confidence: 99%

EARL—Embodied Agent-Based Robot Control Systems Modelling Language

et al. 2020

View full text Add to dashboard Cite

The paper presents the Embodied Agent-based Robot control system modelling Language (EARL). EARL follows a Model-Driven Software Development approach (MDSD), which facilitates robot control system development. It is based on a mathematical method of robot controller specification, employing the concept of an Embodied Agent, and a graphical modelling language: System Modelling Language (SysML). It combines the ease of use of SysML with the precision of mathematical specification of certain aspects of the designed system. It makes the whole system specification effective, from the point of view of the time needed to create it, conciseness of the specification and the possibility of its analysis. By using EARL it is possible to specify systems both with fixed and variable structure. This was achieved by introducing a generalised system model and presenting particular structures of the system in terms of modelling block configurations adapted by using instances. FABRIC framework was created to support the implementation of EARL-based controllers. EARL is compatible with component based robotic middlewares (e.g., ROS and Orocos).

show abstract

Data and performance profiles applying an adaptive truncation criterion, within linesearch-based truncated Newton methods, in large scale nonconvex optimization

Cited by 9 publications

References 7 publications

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

Issues on the use of a modified Bunch and Kaufman decomposition for large scale Newton’s equation

EARL—Embodied Agent-Based Robot Control Systems Modelling Language

Contact Info

Product

Resources

About