An Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Optimization

2014 ◽  
Vol 24 (3) ◽  
pp. 1041-1074 ◽  
Author(s):  
Frank E. Curtis ◽  
Travis C. Johnson ◽  
Daniel P. Robinson ◽  
Andreas Wächter
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Algorithm ◽  
Quadratic Optimization ◽  
Sequential Quadratic Optimization

Task dependent synthesis of some geometrical parameters of a robot mechanism

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 167-171 ◽  
Author(s):  
Maks Oblak ◽  
Karl Gotlih
Keyword(s):  
Mathematical Model ◽  
Nonlinear Optimization ◽  
Optimization Algorithm ◽  
Kinematic Chain ◽  
Chain Structure ◽  
Geometrical Parameters ◽  
Task Space ◽  
End Effector ◽  
Optimal Mechanism ◽  
Nonlinear Optimization Algorithm

SUMMARYThis paper deals with the synthesis of a robot mechanism, which has an open kinematic chain structure. The aim of the synthesis is to find optimal mechanism link lengths and the elevation of the robot mechanism base, with respect to the arbitrary chosen task which is described in a task space.A mathematical model, which describes the problem and enables one to use a nonlinear optimization algorithm, was developed. The usefulness of the approach is demonstrated by the example of the Manutec r3 mechanism with a prescribed task for the robot's end-effector.

Parameter Estimation for an Internal Variable Model Using Nonlinear Optimization and Analytical/Numerical Response Sensitivities

1997 ◽  
Vol 119 (4) ◽  
pp. 337-345 ◽  
Author(s):  
A. F. Fossum
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Optimization ◽  
Optimization Algorithm ◽  
Plastic Material ◽  
General Procedure ◽  
Estimation Procedure ◽  
Variable Model ◽  
Material Parameters ◽  
Relative Response ◽  
Efficient Test

This paper demonstrates through examples that erroneous material constants for complex visco-plastic material models can be obtained from simultaneous parameter estimation by nonlinear optimization methods unless the laboratory load paths used in the fitting process give significant model response sensitivities to changes in all of the material parameters. A general procedure is proposed in which a nonlinear optimization algorithm is coupled with analytically/numerically derived response sensitivities to evaluate an unambiguous set of material parameters. Response sensitivities enter into the parameter estimation procedure in two ways. Relative response sensitivities are first used to identify an efficient test matrix that, when simulated with the model, give model responses that are sensitive to changes in each of the material parameters. Then the corresponding nonzero response sensitivities are used to construct the gradient and Hessian matrices in a gradient-driven optimization algorithm to evaluate the material parameters. A model for braze alloys is used to demonstrate that erroneous parameter values may result if not all of the relative response sensitivities are “nonzero” and distinct.

Nonlinear Optimization Algorithm for Multivariate Optical Element Design

2002 ◽  
Vol 56 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Olusola O. Soyemi ◽  
Frederick G. Haibach ◽  
Paul J. Gemperline ◽  
Michael L. Myrick
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Algorithm ◽  
Optical Computing ◽  
Chemical Species ◽  
Principal Component Regression ◽  
Principal Component ◽  
Optical Element ◽  
Optical Elements ◽  
Design Algorithm ◽  
Nonlinear Optimization Algorithm

A new algorithm for the design of optical computing filters for chemical analysis, otherwise known as multivariate optical elements (MOEs), is described. The approach is based on the nonlinear optimization of the MOE layer thicknesses to minimize the standard error in sample prediction for the chemical species of interest using a modified version of the Gauss–Newton nonlinear optimization algorithm. The design algorithm can either be initialized with random layer thicknesses or with layer thicknesses derived from spectral matching of a multivariate principal component regression (PCR) vector for the constituent of interest. The algorithm has been successfully tested by using it to design various MOEs for the determination of Bismarck Brown dye in a binary mixture of Crystal Violet and Bismarck Brown.

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