Adding a new solver – pracmanm | Testing the result | Conclusion

What does nlsr do? | Output object | Jacobian calculation | Stabilization of Gauss-Newton computations | Programming language | An illustrative example | Problem setup | Solution attempts with nls() | Solution attempts with nlsr tools | Solution attempts with minpack.lm | Solution attempts with wrapnlsr() wrapper | Commentary | Extracting standard errors from nlsr solutions | selfStart options | SSlogisJN.R for the 3-parameter logistic | Running selfStart models with nlxb() | Starting parameters for the Logistic3U model | Jacobian computation | Bounds constraints on parameters | Functional specification of nonlinear least squares problems | Weighted nonlinear regression | Static weights | Weights that are functions of the model parameters | Models that use multiple functional forms | Two straight lines | The WOOD test function | Ongoing efforts | References

Overview and objectives | 0. Issues remaining to address and TODOS | nls() uses different models with different algorithm choices | MINOR -- Bounds specification and warnings for nlsLM and nls.lm | MINOR -- nlsLM and nls.lm do not warn of out of bounds initial parameters | Bounded minimization with minpack.lm | TODOS | 1. Summary of capabilities and functions in nlsr | nlxb | model2rjfun, model2ssgrfun, modelexpr | nlfb -- minimize nonlinear least squares residual functions | coef.nlsr | print.nlsr | summary.nlsr | wrapnlsr | resgr, resss | nlsDeriv, codeDeriv, fnDeriv, newDeriv | nlsSimplify and related functions | 2. Analytic versus approximate Jacobians | Specifying approximations to nlfb | Specifying Jacobian approximations to nlxb | 3. Weighted nonlinear regression | Static weights | Dynamic weights via the wfct() function | Weights built into a one-sided model function | 4. Relative offset and other convergence criteria | Overview of the ROCC test | Some implementation ideas for the ROCC | Other convergence and termination tests | 5. Implementation of nonlinear least squares methods | Gauss-Newton variants | Choices | Using matrix decompositions | 6. Fixed parameters | Motivation for fixed parameters | Background for fixed parameters | Internal structures to specify fixed parameters | Proposed approaches to fix parameters | Examples of use of fixed parameters | 7. Capabilities added to nlsr in the 2022 version | Numerical approximations to Jacobians | Self start models | Models with partially linear parameters | 8. Capabilities still missing from nlsr | Automatic differentiation of functional models | Indexed parameters | 9. Nonlinear equations and other non-modelling problems | Appendix A: Providing exogenous data | Appendix B: Derivative approximation in nls() | From nls.R | From nls.c | nlsr::numericDerivR.R | Appendix C: A comparison of nlsr::nlxb with nls and minpack::nlsLM | Principal differences | Derivative information | Consequences of different derivative computations | Timing comparisons | Programmatic modelling functions | Functional expression of residuals and Jacobian | Marquardt stabilization | Criterion used to terminate the iteration | Output of the modelling functions | Prediction | An illustrative nonlinear regression problem | nls | nlsr | minpack.lm | Problems that are NOT regressions | A check on the Brown and Dennis calculation via function minimization | References

Available analytic differentiation tools | How the tools are used | stats (i.e., the base R installation) | nlsr | Deriv | Ryacas | Derivatives and simplifications -- base R | Derivatives and simplifications -- package nlsr | Derivatives table | Notes: | Simplifying algebraic expressions | Derivatives and simplifications -- package Deriv | Simplifications | Comparison with other approaches | check modelexpr() works with an ssgrfun ?? | test model2rjfun vs model2rjfunx ?? | Need more extensive discussion of Simplify?? | Issues of programming on the language | Another issue: | Indexed parameters or variables | References

Motivation | Background | Internal structures | Proposed algorithmic approaches | Examples of use | For optimx | An extensible bell-curve model | References

Available analytic differentiation tools | How the tools are used | stats (i.e., the base R installation) | nlsr | Deriv | Ryacas | Derivatives and simplifications -- base R | Derivatives and simplifications -- package nlsr | Derivatives table | Notes: | Simplifying algebraic expressions | Derivatives and simplifications -- package Deriv | Simplifications | Comparison with other approaches | check modelexpr() works with an ssgrfun ?? | test model2rjfun vs model2rjfunx ?? | Need more extensive discussion of Simplify?? | Issues of programming on the language | Indexed parameters or variables | Appendix D: A comparison of nlsr::nlxb with nls and minpack::nlsLM | Principal differences | Derivative information | Consequences of different derivative computations | Timing comparisons | Programmatic modelling functions | Functional expression of residuals and Jacobian | Marquardt stabilization | Criterion used to terminate the iteration | Output of the modelling functions | Prediction | An illustrative nonlinear regression problem | nls | minpack.lm | Problems that are NOT regressions | A check on the Brown and Dennis calculation via function minimization | References

Abstract | General Approach | Line Search | Approximate derivatives | Bounds and masks constraints | Checking input information | Steepest descents | Newton-like methods | Variable Metric and quasi-Newton methods | Conjugate Gradient methods | Other ideas for simplifying Newton's method | Acknowledgement | References

Abstract | Background | ``Optimization'' | Intent of package optimx | Unifying the syntax | More than one method at a time | Developments of the optimx() function | Running multiple methods – opm() | Polyalgorithms – multiple methods in sequence | Multiple sets of starting parameters | Bounds | Function and parameter scaling | Access to solver-specific controls | Derivatives | Legacy optimx() function | Solvers provided with the optimx package | Some other functions in the package | Functions that were formerly in the optextras package | References

Rvmmin description, examples and tests

Safeguarded Newton algorithms | The basic approach | Motivations | Some algorithm possibilities | Computing the search vector | Bounds and masks constraints | Examples | An assessment

Abstract | Background | ``Optimization'' | Developments of the optimx() function | How the optimr() function (generally) works | Issues in adding a new method | Running multiple methods | Polyalgorithms – multiple methods in sequence | Multiple sets of starting parameters | Derivatives | Structuring the optimr() function | Functions besides optimr() in the package | Functions that were formerly in the optextras package | Program inefficiencies | Providing controls to different algorithms | Testing the package | References