A brief survey of methods for solving nonlinear least-squares problems

DOI10.3934/naco.2019001zbMath1477.65094OpenAlexW2897250035WikidataQ128963780 ScholiaQ128963780MaRDI QIDQ2273095

Sandra Augusta Santos, Hassan Mohammad, Mohammed Yusuf Waziri

Publication date: 18 September 2019

Published in: Numerical Algebra, Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/naco.2019001

zbMATH Keywords

nonlinear least squaresderivative-free methodsstructured quasi-Newton methodshybridization methodssizing techniques

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Methods of quasi-Newton type (90C53)

Related Items (6)

On the Barzilai–Borwein gradient methods with structured secant equation for nonlinear least squares problems ⋮ Structured two-point stepsize gradient methods for nonlinear least squares ⋮ A survey of gradient methods for solving nonlinear optimization ⋮ Unnamed Item ⋮ Structured spectral algorithm with a nonmonotone line search for nonlinear least squares ⋮ Structured diagonal Gauss-Newton method for nonlinear least squares

Cites Work

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• Local analysis of a spectral correction for the Gauss-Newton model applied to quadratic residual problems
• Jacobian-free implicit inner-iteration preconditioner for nonlinear least squares problems
• On the local convergence of a derivative-free algorithm for least-squares minimization
• A secant method for nonlinear least-squares minimization
• On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization
• Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
• Recent advances in numerical methods for nonlinear equations and nonlinear least squares
• Regularized nonlinear least squares methods for hit position reconstruction in small gamma cameras
• A derivative free iterative method for solving least squares problems
• Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems
• Numerical experiments with variations of the Gauss-Newton algorithm for nonlinear least squares
• Hybrid method for nonlinear least-square problems without calculating derivatives
• Factorized quasi-Newton methods for nonlinear least squares problems
• Solving the nonlinear least square problem: Application of a general method
• Quadratic and superlinear convergence of the Huschens method for nonlinear least squares problems
• A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• A Levenberg--Marquardt scheme for nonlinear image registration
• A globally convergent method for nonlinear least-squares problems based on the Gauss-Newton model with spectral correction
• A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares
• On an iterative algorithm of order 1.839\(\dots\) for solving the nonlinear least squares problems
• Hybrid methods for large sparse nonlinear least squares
• Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems
• On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds
• Algebraic rules for computing the regularization parameter of the Levenberg-Marquardt method
• Optimization theory and methods. Nonlinear programming
• Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation
• Global complexity bound of the Levenberg–Marquardt method
• On the Evaluation Complexity of Cubic Regularization Methods for Potentially Rank-Deficient Nonlinear Least-Squares Problems and Its Relevance to Constrained Nonlinear Optimization
• Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
• Global Convergence of a New Hybrid Gauss–Newton Structured BFGS Method for Nonlinear Least Squares Problems
• A Derivative-Free Algorithm for Least-Squares Minimization
• Structured symmetric rank-one method for unconstrained optimization
• The Modified Gauss-Newton Method for the Fitting of Non-Linear Regression Functions by Least Squares
• Evaluating Derivatives
• Variational Methods for Non-Linear Least-Squares
• Hybrid Methods for Nonlinear Least Squares
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Dud, A Derivative-Free Algorithm for Nonlinear Least Squares
• Some Recent Approaches to Solving Large Residual Nonlinear Least Squares Problems
• An Adaptive Nonlinear Least-Squares Algorithm
• NUMERICAL COMPARISON AMONG STRUCTURED QUASI-NEWTON METHODS FOR NONLINEAR LEAST SQUARES PROBLEMS
• On the selection of parameters in Self Scaling Variable Metric Algorithms
• Specialised versus general-purpose algorithms for minimising functions that are sums of squared terms
• Self-Scaling Variable Metric (SSVM) Algorithms
• The estimation of the hessian matrix in nonlinear least squares problems with non-zero residuals
• On the Use of Product Structure in Secant Methods for Nonlinear Least Squares Problems
• Separable nonlinear least squares: the variable projection method and its applications
• A Family of Scaled Factorized Broyden-Like Methods for Nonlinear Least Squares Problems
• A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
• A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares
• On Large Scale Nonlinear Least Squares Calculations
• Convergence of a Factorized Broyden-Like Family for Nonlinear Least Squares Problems
• On the Evaluation Complexity of Constrained Nonlinear Least-Squares and General Constrained Nonlinear Optimization Using Second-Order Methods
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• Modified Gauss–Newton scheme with worst case guarantees for global performance
• Approximate Gauss–Newton Methods for Nonlinear Least Squares Problems
• A Method for Minimizing a Sum of Squares of Non-Linear Functions Without Calculating Derivatives
• A New Method for Minimising a Sum of Squares without Calculating Gradients
• A method for the solution of certain non-linear problems in least squares
• A modified BFGS method and its global convergence in nonconvex minimization

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