Index

  1. .C
  2. .Call
  3. .External
  4. .Fortran
  5. 1D minimizer, see minimization
    1. one dimensional
  6. 1D roots, see roots
    1. one dimensional
  7. 6–12 potential, see Lennard-Jones potential
  8.  
  9. acknowledgements
  10. active set
    1. see constraint
      1. active set
  11. AD, see automatic differentiation
  12. AD Model Builder, see ADMB
  13. adagio
  14. ADMB
    1. phases (fixed parameters)
  15. alabama
  16. algorithm
    1. controls for
  17. Anstee R
  18. approximate and descend
  19. approximation problem
  20. argument
  21. auglag()
  22. automatic differentiation, Automatic Differentiation Model Builder, see ADMB CRAN
  23. axial search
  24.  
  25. barrier function
    1. logarithmic
  26. BASIC
  27. Bates D
  28. Bayesian inference using Gibbs sampling, see BUGS Markow chain Monte Carlo,
  29. BB
  30. bbmle
  31. Beale–Sorenson method
  32. bell-shaped curve
  33. BFGS
  34. BFGS update
  35. binomial theorem
  36. bisection
  37. bobyqa()
  38. Bolker B
  39. Bolstad J
  40. Borchers H W
  41. bounds, see constraint
  42. box constraint, see constraint
    1. bounds
  43. Box G.
  44. Brent R
  45. Broyden–Fletcher–Goldfarb–Shanno update, see BFGS,
  46. BUGS
  47. byte-code compiler
  48.  
  49. C
  50. Canada Interest Act
  51. Cauchy A-L
  52. centering
  53. CG
  54. CG, see conjugate gradients
  55. checking computations
  56. checks
    1. software
  57. classification
    1. problems
  58. Cobb–Douglas production function
  59. coef()
  60. codecoef()
  61. coefficient, see parameters
  62. coefficients
    1. extracting from solution
  63. COIN-OR
  64. compiler
  65. Comprehensive R Archive Network
  66. computable function
  67. computational efficiency, see efficiency
    1. computational
  68. computational performance, see performance
  69. confidentiality problem
  70. conjugate gradients
  71. Conn A
  72. constraint
    1. active set
    2. bounds
    3. equality
      1. elimination
      2. penalty method
    4. for L1 regression
    5. general
    6. inequality
    7. linear
    8. nonlinear
    9. nonnegativity
    10. parameter elimination
    11. satisfied
    12. unstated
    13. violated
    14. violation
  73. constraint-based optimization, see mathematical programming,
  74. constrOptim.nl()
  75. contour plot
  76. control defaults
  77. controls
    1. optimizer
  78. convergence
    1. quadratic
  79. convergence test
    1. relative offset criterion
  80. convergence tolerance
  81. convex optimization
  82. CPLEX
  83. CRAN
  84. cross-entropy method
  85. crossprod()
  86. curve()
  87.  
  88. Dantzig G
  89. data
    1. exogenous
    2. global
  90. Davidon–Fletcher–Powell update, see DFP
  91. default control settings
  92. Dekker T
  93. Dennis J
  94. DEoptim
  95. derivative
    1. analytic
    2. approximation
      1. with constraint
    3. automatic
    4. backward
    5. central
    6. complex step
    7. example code
    8. forward
    9. incorrect
    10. methods
      1. comparison
    11. numerical
    12. Richardson extrapolation
    13. strategy
    14. symbolic
    15. tools
  96. derivative-free method
  97. deSolve
  98. deviance()
  99. dfoptim
  100. d foptim
  101. DFP
  102. diet problem
  103. differential equation models
  104. differential evolution
  105. differentiation
    1. symbolic
    2. tools
  106. digit cancellation
  107. dimension
    1. reduction by constraint
  108. dput()
  109. Duggleby R
  110. dyn.load()
  111. dyn.load
  112.  
  113. effective monthly interest rate
  114. efficiency
    1. computational
  115. eigen()
  116. Eisenberg M
  117. equality
    1. test for
  118. equality constraint
  119. equation
    1. nonlinear
    2. one variable
    3. system of
  120. error
    1. sign of result
  121. evolutionary operation
  122. execution profile, see profiling
  123. execution time, see timing
  124. exogenous data
  125. expit
  126. expm
  127. exponential function
  128. external tools
    1. linking to
  129.  
  130. failure of computations
  131. feasible region
  132. fitdistr()
  133. fitdistrplus
  134. fixed parameters, see masks, see masks constraint276
  135. Fletcher R
  136. Fletcher–Reeves method
  137. Fortran
  138. free libre software
  139. free parameters
  140. function
    1. computable
    2. external language compiled
    3. undefined
      1. example
  141. function names
    1. confusion
    2. confusion of
    3. duplicate
  142.  
  143. GA
  144. gaoptim
  145. Gauss C-F
  146. Gauss–Newton method
  147. Gaussian density
  148. gaussNewton()
  149. Gay D
  150. generalized inverse
  151. generalized Rosenbrock function, see Rosenbrock function,
  152. genetic optimization methods
  153. GenSA
  154. Geyer C
  155. global minimum
  156. global optimization
  157. gnm
  158. Gnu Linear Programming Kit, see Rglpk
  159. goal of book
  160. Golden-section search
  161. Golub G
  162. gradient
  163. gradient method
  164. GrassmannOptim
  165. grid search
  166. grofit
  167. Grothendieck G
  168.  
  169. Hansen E
  170. Hartley's method
  171. Hassan problem
  172. Hessian
    1. eigenvalues
    2. positive definite
    3. reporting
    4. singular
    5. when bounds active
  173. Hessian matrix, see Hessian
  174. heuristic search
  175. hjk()
  176. hjkb()
  177. Hobbs D
  178. Hobbs weed infestation problem
  179. Hompack
  180. Hooke and Jeeves method
  181. Huet S
  182. hyperbolic transformation
  183.  
  184. inadmissible inputs
  185. inadmissible results
  186. indicator vector
  187. inexact Newton method
  188. infeasible region
  189. infeasible starting point
  190. initial point, see starting point
  191. integer programming
  192. interface
    1. software, see software interfaces
    2. to optimization
  193. interior point optimizer
  194. interpolation
    1. inverse
  195. interval analysis
  196. inverse interpolation, see interpolation
    1. inverse Brent R
  197. ipop()
  198. ipopt()
  199. ipoptr
  200. is.loaded()
  201. iterations
  202. iterative algorithm
  203.  
  204. Jacobian
    1. approximation
    2. singular
    3. singular values
  205. Jacobian matrix, see Jacobian
  206. JAGS
  207. Joe H
  208. Johnson S
  209. Johnson S G,  
  210. Karush W
  211. Kaufman L
  212. Kelley T
  213. kernlab
  214. KKT conditions
    1. see optimality conditions
  215. knitr
  216. Koenker R
  217. Kovalchik S
  218. Krogh F
  219. Kuhn H W
  220.  
  221. L-BFGS-B
  222. L-infinity regression, see minimax regression
  223. L1 norm
  224. L1 regression
  225. L1linreg()
  226. L2 norm
  227. LAD regression, see L1 regression
  228. Lanczos C
  229. Least Absolute Deviations regression, see L1 regression
  230. least squares
    1. for nonlinear equations
    2. linear constraints
    3. nonlinear, see nonlinear least squares
  231. legal issues for R software
  232. Legendre A-M
  233. Lemoine N
  234. Lennard–Jones potential
  235. Levenberg Marquardt stabilization
  236. LEXPIT model
  237. likelihood
  238. likelihood function
    1. gradient
  239. limited memory method
  240. Limited-memory BFGS, see L-BFGS-B
  241. line-search
  242. Linear programming
    1. for L1 regression
  243. linearity
    1. partial
  244. linking
    1. to external tools
    2. via files
  245. linprog
  246. Linux
  247. local minimum
  248. log
    1. of objective function
  249. log likelihood
  250. log scaling
  251. log transformation
  252. logarithmic barrier function
  253. logistic growth model, see model, logistic growth
  254. logistic regression
  255. logit
  256. loops
    1. for
    2. while
    3. avoiding
  257. LP, see Linear Programming
  258. lpSolve
  259. LSODA differential equation solver
  260. Lyness J
  261.  
  262. Maechler M
  263. Markow chain Monte Carlo
  264. Marquardt D
  265. Marquardt method
  266. masks (fixed parameters)
  267. MASS
  268. mathematical programming
  269. Matrix
  270. matrix
    1. $n=1$
  271. matrix multiplication
    1. implicit
  272. maximization, see minimization224
  273. maximum absolute error
  274. maximum absolute residual
    1. see minimax regression
  275. maximum likelihood, see likelihood function143
  276. maxLik
  277. mcga
  278. measures of performance
  279. method
    1. change of
    2. controls for
  280. Michaelis-Menten model
  281. microbenchmark
  282. Microsoft Windows
  283. minima
    1. multiple, see multiple minima
  284. Minimax approximation
  285. minimax regression
    1. by linear programming
  286. minimization
    1. constrained
    2. for nonlinear equations
    3. gradient method
    4. one dimensional
    5. one parameter
    6. unconstrained
  287. minimum
    1. from root-finding
    2. one dimensional
  288. minimum sum of absolute residuals, see L1 regression
  289. minpack.lm
  290. minqa
  291. missing data
    1. leading to termination
  292. mixed effect model
  293. mixed integer programming
  294. mle2()
  295. model
    1. cholera outbreak
    2. LEXPIT
    3. linear
    4. logistic growth
    5. mixed effect
    6. SIWR
  296. model2grfun()
  297. model2jacfun()
  298. model2resfun()
  299. model2ssfun()
  300. modgr()
  301. modss()
  302. monitor progress
  303. mortgage rate
    1. Canada
  304. MOSEK
  305. Mullen K
  306. multinomial maximum likelihood problem
  307. multiple exponentials problem
  308. multiple minima
  309. multiple starts
  310. Murdoch D
  311.  
  312. names for quantities
    1. confusion
  313. Nash J C
  314. negative log likelihood, see likelihood function
  315. Nelder J
  316. Nelder–Mead method
  317. NEOS server
  318. newt1d()
  319. Newton I
  320. Newton's method
  321. Newton's method
    1. difficulties
    2. one dimensional
  322. newuoa()
  323. NISTnls
  324. nleqslv
  325. nlfb()
  326. nlm()
  327. nlme
  328. nlminb()
  329. nlmrt
  330. nlmrt the model expression and generate R functions:,
  331. nlmrt
  332. NLopt
  333. nloptr
  334. nloptwrap
  335. NLP, see nonlinear programming
  336. nlrq()
  337. nls()
    1. plinear algorithm
  338. nls()
  339. nls() ‘port’ algorithm
    1. concerns with
    2. example
    3. structure of solution
  340. nls.lm()
  341. nls2
  342. nlsLM()
  343. nlstools
  344. nlsystemfit()
  345. nlxb()
  346. nlxb
  347. nmk()
  348. nmkb()
  349. nnet()
  350. nnls
  351. nnls, see nonnegative least squares
  352. Nocedal J
  353. nonlinear
  354. nonlinear equations
    1. by minimization
    2. by nonlinear least squares
  355. nonlinear function minimization
  356. nonlinear least squares
    1. ancillary tools
    2. bounds
    3. extreme example
    4. for nonlinear equations
    5. Jacobian
    6. modeling expression
      1. conversion to function
    7. relative offset termination test
    8. residual function
    9. self starting models
    10. small sumsquares termination test
    11. starting parameters
    12. strategies
    13. zero residual problem
  357. nonlinear model
    1. generalized
  358. nonlinear programming
    1. packages
  359. nonlinear regression
  360. nonlinearity
  361. nonnegative least squares
  362. normal density, see Gaussian density
  363. nsga2R
  364. numDeriv
  365.  
  366. obfuscating published statistics
  367. objective function
    1. Fortran
    2. fuzzy
    3. imprecise
    4. imprecisely evaluated
    5. log scale
    6. noisy
    7. properties
    8. quadratic
    9. structure
  368. Oleary D
  369. one-parameter roots, see roots
    1. one dimensional
  370. open source software
  371. OpenBUGS
  372. opposite sign requirement
  373. optextras
  374. optim()
  375. optim() BFGS
  376. optimality conditions
  377. optimization
    1. convex
    2. general constrained
    3. global
    4. stochastic
    5. trajectory
  378. optimize()
    1. example
  379. optimizer project (R-forge)
  380. optimizer controls
  381. optimx
  382. optplus
  383. outer product
  384.  
  385. package
    1. upgrade
  386. package stats
  387. pander
  388. parallel tempering
  389. parameter
    1. extracting from solution
    2. free
  390. parameter elimination
  391. parma
  392. partial linearity
  393. particle swarm algorithms
  394. paster regrowth problem
  395. pattern search
  396. PBSadmb
  397. penalty
    1. sequential increasing
  398. penalty methods
    1. ill-conditioning
  399. Pereyra V
  400. performance
    1. improvement
    2. measures
  401. performance calibration
    1. example
  402. performance tuning, see tuning
  403. pkgucminf
  404. Polak–Ribiére method
  405. polynom
  406. polynomial approximation
  407. polynomial roots
  408. polyroot()
  409. polytope
  410. Powell M J D
  411. pracma
  412. predicted variable
  413. predictor variable
  414. premature termination
  415. Price K
  416. print()
  417. probability collectives
  418. /proc/cpuinfo
  419. /proc/meminfo
  420. production function
  421. profiling
  422. profr
  423. programming style
  424. progress monitoring
  425. project optimizer (R-forge)
  426. projection
  427. proprietary software
  428.  
  429. QP, see quadratic programming
  430. quadprog
  431. quadratic convergence, see convergence
    1. quadratic
  432. Quadratic Programming
  433. quantile regression
    1. nonlinear
  434. quantreg
  435. quantreg Koenker R
  436. quantum annealing
  437. quasi-Newton method
  438.  
  439. R
  440. R
    1. base system
  441. R formula object
  442. R-forge
  443. R2admb
  444. random search
  445. Ratkowsky D
  446. Rayleigh quotient
    1. timings
  447. rbenchmark
  448. Rcgmin
  449. R cgmin
  450. RcplexCPLEX
  451. RcppDE
  452. Rdonlp2
  453. reactive search optimization
  454. regression
    1. versus least squares
  455. relative offset convergence test
    1. see convergence test
      1. relative offset criterion
  456. reliability
  457. Remez algorithm
  458. reparameterization
  459. reportr
  460. require()
  461. residuals
  462. results
    1. inadmissible
    2. output of
  463. results output
  464. return code
  465. rgenoud
  466. Rglpk
  467. rgp rgp
  468. Rmalschains
  469. Rmosek
  470. Rmpfr
  471. robustness
    1. of nonlinear least squares methods
    2. of optimization
  472. root1d()
  473. rootoned (R -forge)
  474. roots
    1. bracketing
    2. complex
    3. example
    4. failure
    5. methods
    6. multiple
    7. one dimensional
    8. polynomial
    9. software requirements
    10. starting interval
  475. Rosenbrock function
    1. generalized
  476. Rprof()
  477. Rsolnp
  478. Rsymphony
  479. Rtools
  480. Runge–Kutta method
  481. Rust B
  482. Rvmmin
  483. R vmmin
  484.  
  485. saddle point
  486. Sande G
  487. SANN
  488. SANN()
  489. scale()
  490. scaling
    1. log, see log scaling likelihood function143
  491. Schnabel R
  492. Seber G
  493. secant method
  494. second derivative matrix, see Hessian
  495. selfStart() methods
  496. sem
  497. separable least squares
  498. separable sums of squares
  499. setRNG
  500. settings
    1. default
  501. shadow price
  502. sign error
  503. simplex
  504. Simplex method (Dantzig)
  505. Simulated Annealing
  506. “singular gradient”
  507. singular Hessian, see Hessian
    1. singular
  508. singular values
    1. Jacobian
  509. singularity
  510. SIWR model
  511. small residuals
  512. smco
  513. software interfaces
  514. software structure
  515. solnp()
  516. solution
    1. acceptable
    2. failure
    3. inadmissible
    4. multiple
    5. test of
    6. unstated constraint
    7. unwanted
    8. user requirements on
  517. Solve.QP()
  518. solver
    1. commercial
  519. soma
  520. speedup, see tuning
  521. spg()
  522. square norm
  523. square transformation
  524. starting interval
  525. starting parameters, see starting point
  526. starting point
    1. infeasible
    2. multiple
  527. starting vector
  528. stats4
  529. steepest descents
    1. example
  530. stepsize
    1. too big
  531. stiff differential equation
  532. stochastic hill climbing
  533. stochastic optimization
  534. stochastic tunneling
  535. structural equations
  536. success indicator
  537. success–failure search
  538. sum of absolute errors
  539. summary()
  540. sumscale problem
  541. SUMT (sequential unconstrained minimization technique)
  542. symbolic differentiation
  543. symbolic differentiation, see differentiation
    1. symbolic
  544. symbolic maths
  545. system call
  546. system()
  547. system.time()
  548. systemfit
  549.  
  550. taboo Search
  551. tanh transformation
  552. termination
    1. abnormal
    2. missing data
  553. termination test
    1. abnormal ending
    2. normal finish
  554. tests
    1. initial
    2. of solution HAI see solution
      1. test of
    3. of solutions
    4. performance loss due to
    5. software
  555. thin client
  556. ∼(tilde)
  557. timing
    1. calibration
    2. example
    3. improvement
    4. of computations
  558. tolerances
  559. tools
  560. Torczon V.
  561. transfinite()
  562. transformation
    1. affine
    2. hyperbolic
    3. log
    4. matrix
    5. square
  563. transformation tanh
  564. truncated Newton method
  565. trust
  566. trustOptim
  567. Tucker A W
  568. tuning, see performance
  569. two straight line problem
  570.  
  571. ucminf
  572. UNCMIN
  573. undefined function, see function
    1. undefined
  574. uniroot
  575. unirootR()
  576. uniroot()
  577. upgrade package, see package
    1. upgrade

     

  578. Varadhan R
  579. variable
    1. dependent
    2. endogenous
    3. exogenous
    4. global
    5. independent
    6. predicted
    7. predictor
  580. variable metric method
  581. variable projection method
  582. VARPRO
  583. vectorization
  584. vectorized code
  585.  
  586. Walster W
  587. Watson L
  588. Watts D
  589. weight loss example
  590. weighted least squares
  591. weighted nonlinear least squares
  592. weighted nonlinear regression
  593. weights
  594. Wickham H
  595. Wild C
  596. WinBUGS
  597. Windows (Microsoft), see Microsoft Windows
  598. WOBLRAMP function
  599. wrapnls()
  600.  
  601. Ypma J
  602.  
  603. zero
    1. test for
  604. zero divide
  605. zeroin()
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