A Few Examples of Least Squares Optimization in Physical Chemistry and Astronomy

1988 ◽  
pp. 327-340
Author(s):  
Edgar Soulie
Keyword(s):  
Physical Chemistry ◽  
Least Squares ◽  
Least Squares Optimization

scholarly journals Method for the identification of explicit polynomial formulae for the friction in turbulent pipe flow

1999 ◽  
Vol 1 (2) ◽  
pp. 115-126 ◽  
Author(s):  
J. W. Davidson ◽  
D. Savic ◽  
G. A. Walters
Keyword(s):  
Least Squares ◽  
Symbolic Regression ◽  
Regression Method ◽  
Turbulent Pipe Flow ◽  
Model Complexity ◽  
Improve Performance ◽  
Rule Based ◽  
Least Squares Optimization ◽  
Starting Solutions ◽  
Crossover And Mutation

The paper describes a new regression method for creating polynomial models. The method combines numerical and symbolic regression. Genetic programming finds the form of polynomial expressions, and least squares optimization finds the values for the constants in the expressions. The incorporation of least squares optimization within symbolic regression is made possible by a rule-based component that algebraically transforms expressions to equivalent forms that are suitable for least squares optimization. The paper describes new operators of crossover and mutation that improve performance, and a new method for creating starting solutions that avoids the problem of under-determined functions. An example application demonstrates the trade-off between model complexity and accuracy of a set of approximator functions created for the Colebrook–White formula.

A Global Weighted Least-Squares Optimization Framework for Speckle Filtering of PolSAR Imagery

2019 ◽  
Vol 57 (3) ◽  
pp. 1265-1277 ◽  
Author(s):  
Yexian Ren ◽  
Jie Yang ◽  
Lingli Zhao ◽  
Pingxiang Li ◽  
Zhiqu Liu ◽  
...  
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Optimization Framework ◽  
Least Squares Optimization ◽  
Speckle Filtering

Optimal Synthesis of a Robomech: Procedure and Application

1999 ◽  
Author(s):  
Stephen Canfield ◽  
Giridhar Kolanupaka ◽  
Ahmad Smaili
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Lagrange Multipliers ◽  
Direct Application ◽  
Optimal Synthesis ◽  
Nonlinear Constraints ◽  
New Class ◽  
Least Squares Optimization ◽  
Synthesis Procedure ◽  
Synthesis Approach

Abstract This paper presents and compares two optimal synthesis techniques for direct application in creating a robomech-II, the second manipulator presented in a new class of linkage arms called Robomcchs. The first optimal synthesis approach will solve the problem as a nonlinear optimization, with a subset of the device parameters described in a linear system and solved directly in a least squares sense. The second approach will employ a least squares optimization using Lagrange Multipliers to contend with nonlinear constraints. In this paper, each optimal synthesis procedure is developed for the general case and then applied to robomcch-II through an example.

scholarly journals Least Squares Optimization: From Theory to Practice

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 51 ◽  
Author(s):  
Giorgio Grisetti ◽  
Tiziano Guadagnino ◽  
Irvin Aloise ◽  
Mirco Colosi ◽  
Bartolomeo Della Corte ◽  
...  
Keyword(s):  
Computer Vision ◽  
Least Squares ◽  
Open Source ◽  
State Of The Art ◽  
Nonlinear Least Squares ◽  
Research Community ◽  
Specific Domain ◽  
Theory To Practice ◽  
Least Squares Optimization ◽  
Computer Vision Systems

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios.

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