{"product_id":"nonlinear-parameter-optimization-using-r-tools-isbn-9781118569283","title":"Nonlinear Parameter Optimization Using R Tools","description":"\u003cp\u003e\u003cb\u003eNonlinear Parameter Optimization Using R\u003c\/b\u003e\u003cbr\u003eJohn C. Nash, Telfer School of Management, University of Ottawa, Canada\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA systematic and comprehensive treatment of optimization software using R\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIn recent decades, optimization techniques have been streamlined by computational and artificial intelligence methods to analyze more variables, especially under non–linear, multivariable conditions, more quickly than ever before.\u003c\/p\u003e \u003cp\u003eOptimization is an important tool for decision science and for the analysis of physical systems used in engineering. Nonlinear Parameter Optimization with R explores the principal tools available in R for function minimization, optimization, and nonlinear parameter determination and features numerous examples throughout.\u003c\/p\u003e \u003cp\u003eNonlinear Parameter Optimization with R:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eProvides a comprehensive treatment of optimization techniques\u003c\/li\u003e \u003cli\u003eExamines optimization problems that arise in statistics and how to solve them using R\u003c\/li\u003e \u003cli\u003eEnables researchers and practitioners to solve parameter determination problems\u003c\/li\u003e \u003cli\u003ePresents traditional methods as well as recent developments in R\u003c\/li\u003e \u003cli\u003eIs supported by an accompanying website featuring R code, examples and datasets\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eResearchers and practitioners who have to solve parameter determination problems who are users of R but are novices in the field optimization or function minimization will benefit from this book. It will also be useful for scientists building and estimating nonlinear models in various fields such as hydrology, sports forecasting, ecology, chemical engineering, pharmaco-kinetics, agriculture, economics and statistics.\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Optimization problem tasks and how they arise 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The general optimization problem 1\u003c\/p\u003e \u003cp\u003e1.2 Why the general problem is generally uninteresting 2\u003c\/p\u003e \u003cp\u003e1.3 (Non-)Linearity 4\u003c\/p\u003e \u003cp\u003e1.4 Objective function properties 4\u003c\/p\u003e \u003cp\u003e1.4.1 Sums of squares 4\u003c\/p\u003e \u003cp\u003e1.4.2 Minimax approximation 5\u003c\/p\u003e \u003cp\u003e1.4.3 Problems with multiple minima 5\u003c\/p\u003e \u003cp\u003e1.4.4 Objectives that can only be imprecisely computed 5\u003c\/p\u003e \u003cp\u003e1.5 Constraint types 5\u003c\/p\u003e \u003cp\u003e1.6 Solving sets of equations 6\u003c\/p\u003e \u003cp\u003e1.7 Conditions for optimality 7\u003c\/p\u003e \u003cp\u003e1.8 Other classifications 7\u003c\/p\u003e \u003cp\u003eReferences 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Optimization algorithms – an overview 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Methods that use the gradient 9\u003c\/p\u003e \u003cp\u003e2.2 Newton-like methods 12\u003c\/p\u003e \u003cp\u003e2.3 The promise of Newton’s method 13\u003c\/p\u003e \u003cp\u003e2.4 Caution: convergence versus termination 14\u003c\/p\u003e \u003cp\u003e2.5 Difficulties with Newton’s method 14\u003c\/p\u003e \u003cp\u003e2.6 Least squares: Gauss–Newton methods 15\u003c\/p\u003e \u003cp\u003e2.7 Quasi-Newton or variable metric method 17\u003c\/p\u003e \u003cp\u003e2.8 Conjugate gradient and related methods 18\u003c\/p\u003e \u003cp\u003e2.9 Other gradient methods 19\u003c\/p\u003e \u003cp\u003e2.10 Derivative-free methods 19\u003c\/p\u003e \u003cp\u003e2.10.1 Numerical approximation of gradients 19\u003c\/p\u003e \u003cp\u003e2.10.2 Approximate and descend 19\u003c\/p\u003e \u003cp\u003e2.10.3 Heuristic search 20\u003c\/p\u003e \u003cp\u003e2.11 Stochastic methods 20\u003c\/p\u003e \u003cp\u003e2.12 Constraint-based methods – mathematical programming 21\u003c\/p\u003e \u003cp\u003eReferences 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Software structure and interfaces 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Perspective 25\u003c\/p\u003e \u003cp\u003e3.2 Issues of choice 26\u003c\/p\u003e \u003cp\u003e3.3 Software issues 27\u003c\/p\u003e \u003cp\u003e3.4 Specifying the objective and constraints to the optimizer 28\u003c\/p\u003e \u003cp\u003e3.5 Communicating exogenous data to problem definition functions 28\u003c\/p\u003e \u003cp\u003e3.5.1 Use of “global” data and variables 31\u003c\/p\u003e \u003cp\u003e3.6 Masked (temporarily fixed) optimization parameters 32\u003c\/p\u003e \u003cp\u003e3.7 Dealing with inadmissible results 33\u003c\/p\u003e \u003cp\u003e3.8 Providing derivatives for functions 34\u003c\/p\u003e \u003cp\u003e3.9 Derivative approximations when there are constraints 36\u003c\/p\u003e \u003cp\u003e3.10 Scaling of parameters and function 36\u003c\/p\u003e \u003cp\u003e3.11 Normal ending of computations 36\u003c\/p\u003e \u003cp\u003e3.12 Termination tests – abnormal ending 37\u003c\/p\u003e \u003cp\u003e3.13 Output to monitor progress of calculations 37\u003c\/p\u003e \u003cp\u003e3.14 Output of the optimization results 38\u003c\/p\u003e \u003cp\u003e3.15 Controls for the optimizer 38\u003c\/p\u003e \u003cp\u003e3.16 Default control settings 39\u003c\/p\u003e \u003cp\u003e3.17 Measuring performance 39\u003c\/p\u003e \u003cp\u003e3.18 The optimization interface 39\u003c\/p\u003e \u003cp\u003eReferences 40\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 One-parameter root-finding problems 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Roots 41\u003c\/p\u003e \u003cp\u003e4.2 Equations in one variable 42\u003c\/p\u003e \u003cp\u003e4.3 Some examples 42\u003c\/p\u003e \u003cp\u003e4.3.1 Exponentially speaking 42\u003c\/p\u003e \u003cp\u003e4.3.2 A normal concern 44\u003c\/p\u003e \u003cp\u003e4.3.3 Little Polly Nomial 46\u003c\/p\u003e \u003cp\u003e4.3.4 A hypothequial question 49\u003c\/p\u003e \u003cp\u003e4.4 Approaches to solving 1D root-finding problems 51\u003c\/p\u003e \u003cp\u003e4.5 What can go wrong? 52\u003c\/p\u003e \u003cp\u003e4.6 Being a smart user of root-finding programs 54\u003c\/p\u003e \u003cp\u003e4.7 Conclusions and extensions 54\u003c\/p\u003e \u003cp\u003eReferences 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 One-parameter minimization problems 56\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The optimize() function 56\u003c\/p\u003e \u003cp\u003e5.2 Using a root-finder 57\u003c\/p\u003e \u003cp\u003e5.3 But where is the minimum? 58\u003c\/p\u003e \u003cp\u003e5.4 Ideas for 1D minimizers 59\u003c\/p\u003e \u003cp\u003e5.5 The line-search subproblem 61\u003c\/p\u003e \u003cp\u003eReferences 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Nonlinear least squares 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 nls() from package stats 63\u003c\/p\u003e \u003cp\u003e6.1.1 A simple example 63\u003c\/p\u003e \u003cp\u003e6.1.2 Regression versus least squares 65\u003c\/p\u003e \u003cp\u003e6.2 A more difficult case 65\u003c\/p\u003e \u003cp\u003e6.3 The structure of the nls() solution 72\u003c\/p\u003e \u003cp\u003e6.4 Concerns with nls() 73\u003c\/p\u003e \u003cp\u003e6.4.1 Small residuals 74\u003c\/p\u003e \u003cp\u003e6.4.2 Robustness – “singular gradient” woes 75\u003c\/p\u003e \u003cp\u003e6.4.3 Bounds with nls() 77\u003c\/p\u003e \u003cp\u003e6.5 Some ancillary tools for nonlinear least squares 79\u003c\/p\u003e \u003cp\u003e6.5.1 Starting values and self-starting problems 79\u003c\/p\u003e \u003cp\u003e6.5.2 Converting model expressions to sum-of-squares functions 80\u003c\/p\u003e \u003cp\u003e6.5.3 Help for nonlinear regression 80\u003c\/p\u003e \u003cp\u003e6.6 Minimizing Rfunctions that compute sums of squares 81\u003c\/p\u003e \u003cp\u003e6.7 Choosing an approach 82\u003c\/p\u003e \u003cp\u003e6.8 Separable sums of squares problems 86\u003c\/p\u003e \u003cp\u003e6.9 Strategies for nonlinear least squares 93\u003c\/p\u003e \u003cp\u003eReferences 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Nonlinear equations 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Packages and methods for nonlinear equations 95\u003c\/p\u003e \u003cp\u003e7.1.1 BB 96\u003c\/p\u003e \u003cp\u003e7.1.2 nleqslv 96\u003c\/p\u003e \u003cp\u003e7.1.3 Using nonlinear least squares 96\u003c\/p\u003e \u003cp\u003e7.1.4 Using function minimization methods 96\u003c\/p\u003e \u003cp\u003e7.2 A simple example to compare approaches 97\u003c\/p\u003e \u003cp\u003e7.3 A statistical example 103\u003c\/p\u003e \u003cp\u003eReferences 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Function minimization tools in the base \u003c\/b\u003eR \u003cb\u003esystem 108\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 optim() 108\u003c\/p\u003e \u003cp\u003e8.2 nlm() 110\u003c\/p\u003e \u003cp\u003e8.3 nlminb() 111\u003c\/p\u003e \u003cp\u003e8.4 Using the base optimization tools 112\u003c\/p\u003e \u003cp\u003eReferences 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Add-in function minimization packages for \u003c\/b\u003eR \u003cb\u003e115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Package optimx 115\u003c\/p\u003e \u003cp\u003e9.1.1 Optimizers in optimx 116\u003c\/p\u003e \u003cp\u003e9.1.2 Example use of optimx() 117\u003c\/p\u003e \u003cp\u003e9.2 Some other function minimization packages 118\u003c\/p\u003e \u003cp\u003e9.2.1 nloptr and nloptwrap 118\u003c\/p\u003e \u003cp\u003e9.2.2 trust and trustOptim 119\u003c\/p\u003e \u003cp\u003e9.3 Should we replace optim() routines? 121\u003c\/p\u003e \u003cp\u003eReferences 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Calculating and using derivatives 123\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Why and how 123\u003c\/p\u003e \u003cp\u003e10.2 Analytic derivatives – by hand 124\u003c\/p\u003e \u003cp\u003e10.3 Analytic derivatives – tools 125\u003c\/p\u003e \u003cp\u003e10.4 Examples of use of R tools for differentiation 125\u003c\/p\u003e \u003cp\u003e10.5 Simple numerical derivatives 127\u003c\/p\u003e \u003cp\u003e10.6 Improved numerical derivative approximations 128\u003c\/p\u003e \u003cp\u003e10.6.1 The Richardson extrapolation 128\u003c\/p\u003e \u003cp\u003e10.6.2 Complex-step derivative approximations 128\u003c\/p\u003e \u003cp\u003e10.7 Strategy and tactics for derivatives 129\u003c\/p\u003e \u003cp\u003eReferences 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Bounds constraints 132\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Single bound: use of a logarithmic transformation 132\u003c\/p\u003e \u003cp\u003e11.2 Interval bounds: Use of a hyperbolic transformation 133\u003c\/p\u003e \u003cp\u003e11.2.1 Example of the tanh transformation 134\u003c\/p\u003e \u003cp\u003e11.2.2 A fly in the ointment 134\u003c\/p\u003e \u003cp\u003e11.3 Setting the objective large when bounds are violated 135\u003c\/p\u003e \u003cp\u003e11.4 An active set approach 136\u003c\/p\u003e \u003cp\u003e11.5 Checking bounds 138\u003c\/p\u003e \u003cp\u003e11.6 The importance of using bounds intelligently 138\u003c\/p\u003e \u003cp\u003e11.6.1 Difficulties in applying bounds constraints 139\u003c\/p\u003e \u003cp\u003e11.7 Post-solution information for bounded problems 139\u003c\/p\u003e \u003cp\u003eAppendix 11.A Function transfinite 141\u003c\/p\u003e \u003cp\u003eReferences 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Using masks 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 An example 143\u003c\/p\u003e \u003cp\u003e12.2 Specifying the objective 143\u003c\/p\u003e \u003cp\u003e12.3 Masks for nonlinear least squares 147\u003c\/p\u003e \u003cp\u003e12.4 Other approaches to masks 148\u003c\/p\u003e \u003cp\u003eReferences 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Handling general constraints 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Equality constraints 149\u003c\/p\u003e \u003cp\u003e13.1.1 Parameter elimination 151\u003c\/p\u003e \u003cp\u003e13.1.2 Which parameter to eliminate? 153\u003c\/p\u003e \u003cp\u003e13.1.3 Scaling and centering? 154\u003c\/p\u003e \u003cp\u003e13.1.4 Nonlinear programming packages 154\u003c\/p\u003e \u003cp\u003e13.1.5 Sequential application of an increasing penalty 156\u003c\/p\u003e \u003cp\u003e13.2 Sumscale problems 158\u003c\/p\u003e \u003cp\u003e13.2.1 Using a projection 162\u003c\/p\u003e \u003cp\u003e13.3 Inequality constraints 163\u003c\/p\u003e \u003cp\u003e13.4 A perspective on penalty function ideas 167\u003c\/p\u003e \u003cp\u003e13.5 Assessment 167\u003c\/p\u003e \u003cp\u003eReferences 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Applications of mathematical programming 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Statistical applications of math programming 169\u003c\/p\u003e \u003cp\u003e14.2 R packages for math programming 170\u003c\/p\u003e \u003cp\u003e14.3 Example problem: L1 regression 171\u003c\/p\u003e \u003cp\u003e14.4 Example problem: minimax regression 177\u003c\/p\u003e \u003cp\u003e14.5 Nonlinear quantile regression 179\u003c\/p\u003e \u003cp\u003e14.6 Polynomial approximation 180\u003c\/p\u003e \u003cp\u003eReferences 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Global optimization and stochastic methods 185\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Panorama of methods 185\u003c\/p\u003e \u003cp\u003e15.2 R packages for global and stochastic optimization 186\u003c\/p\u003e \u003cp\u003e15.3 An example problem 187\u003c\/p\u003e \u003cp\u003e15.3.1 Method SANN from optim() 187\u003c\/p\u003e \u003cp\u003e15.3.2 Package GenSA 188\u003c\/p\u003e \u003cp\u003e15.3.3 Packages DEoptim and RcppDE 189\u003c\/p\u003e \u003cp\u003e15.3.4 Package smco 191\u003c\/p\u003e \u003cp\u003e15.3.5 Package soma 192\u003c\/p\u003e \u003cp\u003e15.3.6 Package Rmalschains 193\u003c\/p\u003e \u003cp\u003e15.3.7 Package rgenoud 193\u003c\/p\u003e \u003cp\u003e15.3.8 Package GA 194\u003c\/p\u003e \u003cp\u003e15.3.9 Package gaoptim 195\u003c\/p\u003e \u003cp\u003e15.4 Multiple starting values 196\u003c\/p\u003e \u003cp\u003eReferences 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Scaling and reparameterization 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Why scale or reparameterize? 203\u003c\/p\u003e \u003cp\u003e16.2 Formalities of scaling and reparameterization 204\u003c\/p\u003e \u003cp\u003e16.3 Hobbs’ weed infestation example 205\u003c\/p\u003e \u003cp\u003e16.4 The KKT conditions and scaling 210\u003c\/p\u003e \u003cp\u003e16.5 Reparameterization of the weeds problem 214\u003c\/p\u003e \u003cp\u003e16.6 Scale change across the parameter space 214\u003c\/p\u003e \u003cp\u003e16.7 Robustness of methods to starting points 215\u003c\/p\u003e \u003cp\u003e16.7.1 Robustness of optimization techniques 218\u003c\/p\u003e \u003cp\u003e16.7.2 Robustness of nonlinear least squares methods 220\u003c\/p\u003e \u003cp\u003e16.8 Strategies for scaling 222\u003c\/p\u003e \u003cp\u003eReferences 223\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Finding the right solution 224\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Particular requirements 224\u003c\/p\u003e \u003cp\u003e17.1.1 A few integer parameters 225\u003c\/p\u003e \u003cp\u003e17.2 Starting values for iterative methods 225\u003c\/p\u003e \u003cp\u003e17.3 KKT conditions 226\u003c\/p\u003e \u003cp\u003e17.3.1 Unconstrained problems 226\u003c\/p\u003e \u003cp\u003e17.3.2 Constrained problems 227\u003c\/p\u003e \u003cp\u003e17.4 Search tests 228\u003c\/p\u003e \u003cp\u003eReferences 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Tuning and terminating methods 230\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Timing and profiling 230\u003c\/p\u003e \u003cp\u003e18.1.1 rbenchmark 231\u003c\/p\u003e \u003cp\u003e18.1.2 microbenchmark 231\u003c\/p\u003e \u003cp\u003e18.1.3 Calibrating our timings 232\u003c\/p\u003e \u003cp\u003e18.2 Profiling 234\u003c\/p\u003e \u003cp\u003e18.2.1 Trying possible improvements 235\u003c\/p\u003e \u003cp\u003e18.3 More speedups of R computations 238\u003c\/p\u003e \u003cp\u003e18.3.1 Byte-code compiled functions 238\u003c\/p\u003e \u003cp\u003e18.3.2 Avoiding loops 238\u003c\/p\u003e \u003cp\u003e18.3.3 Package upgrades - an example 239\u003c\/p\u003e \u003cp\u003e18.3.4 Specializing codes 241\u003c\/p\u003e \u003cp\u003e18.4 External language compiled functions 242\u003c\/p\u003e \u003cp\u003e18.4.1 Building an R function using Fortran 244\u003c\/p\u003e \u003cp\u003e18.4.2 Summary of Rayleigh quotient timings 246\u003c\/p\u003e \u003cp\u003e18.5 Deciding when we are finished 247\u003c\/p\u003e \u003cp\u003e18.5.1 Tests for things gone wrong 248\u003c\/p\u003e \u003cp\u003eReferences 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Linking \u003c\/b\u003eR \u003cb\u003eto external optimization tools 250\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Mechanisms to link R to external software 251\u003c\/p\u003e \u003cp\u003e19.1.1 R functions to call external (sub)programs 251\u003c\/p\u003e \u003cp\u003e19.1.2 File and system call methods 251\u003c\/p\u003e \u003cp\u003e19.1.3 Thin client methods 252\u003c\/p\u003e \u003cp\u003e19.2 Prepackaged links to external optimization tools 252\u003c\/p\u003e \u003cp\u003e19.2.1 NEOS 252\u003c\/p\u003e \u003cp\u003e19.2.2 Automatic Differentiation Model Builder (ADMB) 252\u003c\/p\u003e \u003cp\u003e19.2.3 NLopt 253\u003c\/p\u003e \u003cp\u003e19.2.4 BUGS and related tools 253\u003c\/p\u003e \u003cp\u003e19.3 Strategy for using external tools 253\u003c\/p\u003e \u003cp\u003eReferences 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Differential equation models 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 The model 255\u003c\/p\u003e \u003cp\u003e20.2 Background 256\u003c\/p\u003e \u003cp\u003e20.3 The likelihood function 258\u003c\/p\u003e \u003cp\u003e20.4 A first try at minimization 258\u003c\/p\u003e \u003cp\u003e20.5 Attempts with optimx 259\u003c\/p\u003e \u003cp\u003e20.6 Using nonlinear least squares 260\u003c\/p\u003e \u003cp\u003e20.7 Commentary 261\u003c\/p\u003e \u003cp\u003eReference 262\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Miscellaneous nonlinear estimation tools for \u003c\/b\u003eR \u003cb\u003e263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Maximum likelihood 263\u003c\/p\u003e \u003cp\u003e21.2 Generalized nonlinear models 266\u003c\/p\u003e \u003cp\u003e21.3 Systems of equations 268\u003c\/p\u003e \u003cp\u003e21.4 Additional nonlinear least squares tools 268\u003c\/p\u003e \u003cp\u003e21.5 Nonnegative least squares 270\u003c\/p\u003e \u003cp\u003e21.6 Noisy objective functions 273\u003c\/p\u003e \u003cp\u003e21.7 Moving forward 274\u003c\/p\u003e \u003cp\u003eReferences 275\u003c\/p\u003e \u003cp\u003eAppendix A R packages used in examples 276\u003c\/p\u003e \u003cp\u003eIndex 279\u003c\/p\u003e \u003cp\u003e\"The book chapters are enriched by little anecdotes, and the reader obviously benefits from John C. Nash's experience of more than 30 years in the field of nonlinear optimization. This experience translates into many practical recommendations and tweaks. The book provides plenty of code examples and useful code snippets.\" (Biometrical \u003ci\u003eJournal\u003c\/i\u003e, 2016)\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eJOHN C. NASH,\u003c\/b\u003e Telfer School of Management, University of Ottawa, Canada   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eNONLINER PARAMETER OPTIMIZATION USING R TOOLS\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eA systematic and comprehensive treatment of optimization software using R\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eOptimization is an important tool for decision science and for the analysis of physical systems used in engineering. \u003ci\u003eNonlinear Parameter Optimization Using R Tools\u003c\/i\u003e explores the principal tools available in R for function minimization, optimization, and nonlinear parameter determination and features numerous examples throughout. \u003c\/p\u003e\u003cp\u003eIn recent decades, optimization techniques have been streamlined by computational and artificial intelligence methods to analyze more variables, especially under nonlinear, multivariable conditions, more quickly than ever before. \u003c\/p\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003eNonlinear Parameter Optimization Using R Tools:\u003c\/i\u003e\u003c\/b\u003e \u003c\/p\u003e\u003cul\u003e \u003cli\u003eProvides a comprehensive treatment of optimization techniques\u003c\/li\u003e \u003cli\u003eExamines optimization problems that arise in statistics and how to solve them using R\u003c\/li\u003e \u003cli\u003eEnables researchers and practitioners to solve parameter determination problems\u003c\/li\u003e \u003cli\u003ePresents traditional methods as well as recent developments in R\u003c\/li\u003e \u003cli\u003eIs supported by an accompanying website featuring R code, examples, and datasets: www.wiley.com\/go\/nonlinear_parameter\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eResearchers and practitioners who have to solve parameter determination problems who are users of R but are novices in the field optimization or function minimization will benefit from this book. It will also be useful for scientists building and estimating nonlinear models in various fields such as hydrology, sports forecasting, ecology, chemical engineering, pharmacokinetics, agriculture, economics, and statistics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989696004325,"sku":"NP9781118569283","price":92.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118569283.jpg?v=1761785141","url":"https:\/\/k12savings.com\/products\/nonlinear-parameter-optimization-using-r-tools-isbn-9781118569283","provider":"K12savings","version":"1.0","type":"link"}