BBoptim: Large=Scale Nonlinear Optimization - A Wrapper for spg()

Description Usage Arguments Details Value References See Also Examples

View source: R/BBoptim.R

Description

A strategy using different Barzilai-Borwein steplengths to optimize a nonlinear objective function subject to box constraints.

Usage

1
2
3
4
  BBoptim(par, fn, gr=NULL, method=c(2,3,1), lower=-Inf, upper=Inf, 
  	project=NULL, projectArgs=NULL,
	control=list(), quiet=FALSE, ...) 
  

Arguments

par

A real vector argument to fn, indicating the initial guess for the root of the nonliinear system of equations fn.

fn

Nonlinear objective function that is to be optimized. A scalar function that takes a real vector as argument and returns a scalar that is the value of the function at that point (see details).

gr

The gradient of the objective function fn evaluated at the argument. This is a vector-function that takes a real vector as argument and returns a real vector of the same length. It defaults to NULL, which means that gradient is evaluated numerically. Computations are dramatically faster in high-dimensional problems when the exact gradient is provided. See *Example*.

method

A vector of integers specifying which Barzilai-Borwein steplengths should be used in a consecutive manner. The methods will be used in the order specified.

upper

An upper bound for box constraints. See spg

lower

An lower bound for box constraints. See spg

project

The projection function that takes a point in $R^n$ and projects it onto a region that defines the constraints of the problem. This is a vector-function that takes a real vector as argument and returns a real vector of the same length. See spg for more details.

projectArgs

list of arguments to project. See spg() for more details.

control

A list of parameters governing the algorithm behaviour. This list is the same as that for spg (excepting the default for trace). See details for important special features of control parameters.

quiet

logical indicating if messages about convergence success or failure should be suppressed

...

arguments passed fn (via the optimization algorithm).

Details

This wrapper is especially useful in problems where (spg is likely to experience convergence difficulties. When spg() fails, i.e. when convergence > 0 is obtained, a user might attempt various strategies to find a local optimizer. The function BBoptim tries the following sequential strategy:

  1. Try a different BB steplength. Since the default is method = 2 for dfsane, BBoptim wrapper tries method = c(2, 3, 1).

  2. Try a different non-monotonicity parameter M for each method, i.e. BBoptim wrapper tries M = c(50, 10) for each BB steplength.

The argument control defaults to a list with values maxit = 1500, M = c(50, 10), ftol=1.e-10, gtol = 1e-05, maxfeval = 10000, maximize = FALSE, trace = FALSE, triter = 10, eps = 1e-07, checkGrad=NULL. It is recommended that checkGrad be set to FALSE for high-dimensional problems, after making sure that the gradient is correctly specified. See spg for additional details about the default.

If control is specified as an argument, only values which are different need to be given in the list. See spg for more details.

Value

A list with the same elements as returned by spg. One additional element returned is cpar which contains the control parameter settings used to obtain successful convergence, or to obtain the best solution in case of failure.

References

R Varadhan and PD Gilbert (2009), BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function, J. Statistical Software, 32:4, http://www.jstatsoft.org/v32/i04/

See Also

BBsolve, spg, multiStart optim grad

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
# Use a preset seed so test values are reproducable. 
require("setRNG")
old.seed <- setRNG(list(kind="Mersenne-Twister", normal.kind="Inversion",
    seed=1234))

rosbkext <- function(x){
# Extended Rosenbrock function
n <- length(x)
j <- 2 * (1:(n/2))
jm1 <- j - 1
sum(100 * (x[j] - x[jm1]^2)^2 + (1 - x[jm1])^2)
}

p0 <- rnorm(50)
spg(par=p0, fn=rosbkext)
BBoptim(par=p0, fn=rosbkext)

# compare the improvement in convergence when bounds are specified
BBoptim(par=p0, fn=rosbkext, lower=0) 

# identical to spg() with defaults
BBoptim(par=p0, fn=rosbkext, method=3, control=list(M=10, trace=TRUE))  

Example output

Loading required package: setRNG
iter:  0  f-value:  10824.77  pgrad:  5320.046 
iter:  10  f-value:  39.77528  pgrad:  27.99759 
iter:  20  f-value:  30.22168  pgrad:  10.38169 
iter:  30  f-value:  26.85768  pgrad:  40.95957 
iter:  40  f-value:  24.2456  pgrad:  2.925454 
iter:  50  f-value:  18.21567  pgrad:  3.079435 
iter:  60  f-value:  14.91738  pgrad:  2.334929 
iter:  70  f-value:  13.44534  pgrad:  11.99571 
iter:  80  f-value:  11.40815  pgrad:  1.799464 
iter:  90  f-value:  9.712975  pgrad:  4.29862 
iter:  100  f-value:  8.392164  pgrad:  11.32991 
iter:  110  f-value:  7.311477  pgrad:  1.565696 
iter:  120  f-value:  6.639707  pgrad:  3.421991 
iter:  130  f-value:  6.193688  pgrad:  22.20667 
iter:  140  f-value:  4.66529  pgrad:  1.574616 
iter:  150  f-value:  3.937451  pgrad:  8.75098 
iter:  160  f-value:  3.153241  pgrad:  6.673114 
iter:  170  f-value:  2.208422  pgrad:  1.53933 
iter:  180  f-value:  1.669985  pgrad:  0.8507576 
iter:  190  f-value:  1.449601  pgrad:  1.953953 
iter:  200  f-value:  1.371948  pgrad:  0.6711463 
iter:  210  f-value:  1.114267  pgrad:  1.776885 
iter:  220  f-value:  0.9583621  pgrad:  1.568243 
iter:  230  f-value:  0.8269146  pgrad:  3.633741 
iter:  240  f-value:  0.6304826  pgrad:  0.3339276 
iter:  250  f-value:  0.5107885  pgrad:  0.2684569 
iter:  260  f-value:  0.4613847  pgrad:  0.2476938 
iter:  270  f-value:  0.3270633  pgrad:  11.01763 
iter:  280  f-value:  0.1742687  pgrad:  0.444439 
iter:  290  f-value:  0.1625566  pgrad:  0.1235645 
iter:  300  f-value:  0.101921  pgrad:  1.459339 
iter:  310  f-value:  0.09256554  pgrad:  0.08955312 
iter:  320  f-value:  0.04521948  pgrad:  0.05963155 
iter:  330  f-value:  0.02634377  pgrad:  0.04566414 
iter:  340  f-value:  0.01193873  pgrad:  0.0904557 
iter:  350  f-value:  0.008038826  pgrad:  0.1842721 
iter:  360  f-value:  0.01248124  pgrad:  3.643765 
iter:  370  f-value:  0.001487418  pgrad:  0.1724186 
iter:  380  f-value:  0.0009728912  pgrad:  0.008121104 
iter:  390  f-value:  0.0001587139  pgrad:  0.003207078 
iter:  400  f-value:  1.091916e-07  pgrad:  4.596227e-05 
$par
 [1] 0.9999292 0.9998582 0.9999353 0.9998704 0.9999426 0.9998850 0.9999344
 [8] 0.9998686 0.9999350 0.9998698 0.9999351 0.9998700 0.9999316 0.9998630
[15] 0.9999404 0.9998806 0.9999350 0.9998699 0.9999125 0.9998247 0.9999356
[22] 0.9998711 0.9999310 0.9998619 0.9999353 0.9998704 0.9999356 0.9998710
[29] 0.9999353 0.9998705 0.9999378 0.9998755 0.9999341 0.9998680 0.9999349
[36] 0.9998695 0.9999350 0.9998697 0.9999347 0.9998693 0.9999360 0.9998718
[43] 0.9999330 0.9998659 0.9999348 0.9998694 0.9999351 0.9998700 0.9999344
[50] 0.9998686

$value
[1] 1.091439e-07

$gradient
[1] 4.597844e-05

$fn.reduction
[1] 10824.77

$iter
[1] 401

$feval
[1] 493

$convergence
[1] 0

$message
[1] "Successful convergence"

iter:  0  f-value:  10824.77  pgrad:  5320.046 
iter:  10  f-value:  54.40324  pgrad:  52.26724 
iter:  20  f-value:  33.13841  pgrad:  2.110108 
iter:  30  f-value:  26.40889  pgrad:  2.109646 
iter:  40  f-value:  18.79585  pgrad:  2.063969 
iter:  50  f-value:  16.09957  pgrad:  2.000223 
iter:  60  f-value:  13.9462  pgrad:  2.576766 
iter:  70  f-value:  12.70453  pgrad:  2.179719 
iter:  80  f-value:  10.25791  pgrad:  2.176441 
iter:  90  f-value:  8.034416  pgrad:  12.35637 
iter:  100  f-value:  7.331731  pgrad:  2.065253 
iter:  110  f-value:  6.600971  pgrad:  1.61036 
iter:  120  f-value:  4.842992  pgrad:  1.517246 
iter:  130  f-value:  4.273633  pgrad:  1.502324 
iter:  140  f-value:  3.519309  pgrad:  17.5416 
iter:  150  f-value:  2.483051  pgrad:  2.053522 
iter:  160  f-value:  3.74858  pgrad:  35.27227 
iter:  170  f-value:  1.095609  pgrad:  0.8585015 
iter:  180  f-value:  1.002489  pgrad:  0.4675539 
iter:  190  f-value:  0.9069942  pgrad:  0.4363785 
iter:  200  f-value:  0.4666699  pgrad:  1.127691 
iter:  210  f-value:  0.3889428  pgrad:  0.2377373 
iter:  220  f-value:  0.07270047  pgrad:  2.09311 
iter:  230  f-value:  0.01169285  pgrad:  0.0282269 
iter:  240  f-value:  0.01127181  pgrad:  1.139276 
  Successful convergence.
$par
 [1] 0.9999683 0.9999366 0.9999685 0.9999369 0.9999687 0.9999373 0.9999684
 [8] 0.9999368 0.9999685 0.9999369 0.9999685 0.9999369 0.9999684 0.9999367
[15] 0.9999686 0.9999372 0.9999685 0.9999369 0.9999682 0.9999363 0.9999685
[22] 0.9999369 0.9999684 0.9999367 0.9999685 0.9999369 0.9999685 0.9999369
[29] 0.9999685 0.9999369 0.9999685 0.9999370 0.9999684 0.9999368 0.9999685
[36] 0.9999369 0.9999685 0.9999369 0.9999685 0.9999369 0.9999685 0.9999369
[43] 0.9999684 0.9999368 0.9999685 0.9999369 0.9999685 0.9999369 0.9999684
[50] 0.9999368

$value
[1] 2.488589e-08

$gradient
[1] 1.617719e-06

$fn.reduction
[1] 10824.77

$iter
[1] 242

$feval
[1] 345

$convergence
[1] 0

$message
[1] "Successful convergence"

$cpar
method      M 
     2     50 

iter:  0  f-value:  10824.77  pgrad:  93589969068 
iter:  10  f-value:  80.17689  pgrad:  89.45276 
iter:  20  f-value:  18.6482  pgrad:  2.331853 
iter:  30  f-value:  16.57026  pgrad:  14.70272 
iter:  40  f-value:  14.53976  pgrad:  1.620273 
iter:  50  f-value:  13.00756  pgrad:  14.99384 
iter:  60  f-value:  12.46553  pgrad:  1.191981 
iter:  70  f-value:  11.5946  pgrad:  1.075108 
iter:  80  f-value:  11.05444  pgrad:  1.007026 
iter:  90  f-value:  10.2394  pgrad:  0.9117447 
iter:  100  f-value:  9.546816  pgrad:  0.8072167 
iter:  110  f-value:  9.009637  pgrad:  0.7865717 
iter:  120  f-value:  8.107801  pgrad:  1.592373 
iter:  130  f-value:  7.803584  pgrad:  0.6117142 
iter:  140  f-value:  7.656692  pgrad:  0.5939561 
iter:  150  f-value:  4.065993  pgrad:  0.4956877 
iter:  160  f-value:  3.959986  pgrad:  0.8255063 
iter:  170  f-value:  3.887696  pgrad:  0.4946903 
iter:  180  f-value:  3.701328  pgrad:  2.09004 
iter:  190  f-value:  3.632759  pgrad:  0.4825317 
iter:  200  f-value:  3.098259  pgrad:  1.007279 
iter:  210  f-value:  3.039008  pgrad:  1.593319 
iter:  220  f-value:  3.018869  pgrad:  0.488434 
iter:  230  f-value:  2.667001  pgrad:  4.129558 
iter:  240  f-value:  2.554116  pgrad:  0.4780626 
iter:  250  f-value:  2.207891  pgrad:  1.591027 
iter:  260  f-value:  1.998948  pgrad:  0.5785394 
iter:  270  f-value:  1.96601  pgrad:  0.4639743 
iter:  280  f-value:  1.934402  pgrad:  0.462478 
iter:  290  f-value:  1.849995  pgrad:  0.5029136 
iter:  300  f-value:  1.834994  pgrad:  0.4596853 
iter:  310  f-value:  1.814697  pgrad:  0.4329975 
iter:  320  f-value:  1.100727  pgrad:  0.6330166 
iter:  330  f-value:  1.091672  pgrad:  0.4246225 
iter:  340  f-value:  1.034675  pgrad:  0.4189956 
iter:  350  f-value:  1.017113  pgrad:  0.4180038 
iter:  360  f-value:  1.00267  pgrad:  0.4166663 
iter:  370  f-value:  0.8821494  pgrad:  7.53588 
iter:  380  f-value:  0.7199736  pgrad:  0.3883554 
iter:  390  f-value:  0.5232619  pgrad:  0.3573914 
iter:  400  f-value:  0.5201436  pgrad:  0.355807 
iter:  410  f-value:  0.4125356  pgrad:  0.3006682 
iter:  420  f-value:  0.4067102  pgrad:  0.3310747 
iter:  430  f-value:  0.4018838  pgrad:  0.3295781 
iter:  440  f-value:  0.3468103  pgrad:  0.3148879 
iter:  450  f-value:  0.2720018  pgrad:  0.2911181 
iter:  460  f-value:  0.2599182  pgrad:  0.2865981 
iter:  470  f-value:  0.258163  pgrad:  0.2861937 
iter:  480  f-value:  0.0674882  pgrad:  0.3424147 
iter:  490  f-value:  0.002635549  pgrad:  0.0397948 
iter:  500  f-value:  0.0003608076  pgrad:  0.01779499 
iter:  510  f-value:  2.282022e-08  pgrad:  0.0006876697 
  Successful convergence.
$par
 [1] 0.9999699 0.9999399 0.9999700 0.9999399 0.9999700 0.9999399 0.9999699
 [8] 0.9999399 0.9999699 0.9999399 0.9999699 0.9999399 0.9999699 0.9999399
[15] 0.9999700 0.9999399 0.9999699 0.9999399 0.9999700 0.9999399 0.9999699
[22] 0.9999399 0.9999699 0.9999399 0.9999699 0.9999399 0.9999700 0.9999399
[29] 0.9999699 0.9999399 0.9999700 0.9999399 0.9999699 0.9999399 0.9999699
[36] 0.9999399 0.9999699 0.9999399 0.9999699 0.9999399 0.9999698 0.9999395
[43] 0.9999699 0.9999399 0.9999699 0.9999399 0.9999699 0.9999399 0.9999699
[50] 0.9999399

$value
[1] 2.259115e-08

$gradient
[1] 1.583901e-07

$fn.reduction
[1] 10824.77

$iter
[1] 513

$feval
[1] 638

$convergence
[1] 0

$message
[1] "Successful convergence"

$cpar
method      M 
     2     50 

iter:  0  f-value:  10824.77  pgrad:  5320.046 
iter:  10  f-value:  39.77528  pgrad:  27.99759 
iter:  20  f-value:  30.22168  pgrad:  10.38169 
iter:  30  f-value:  26.85768  pgrad:  40.95957 
iter:  40  f-value:  24.2456  pgrad:  2.925454 
iter:  50  f-value:  18.21567  pgrad:  3.079435 
iter:  60  f-value:  14.91738  pgrad:  2.334929 
iter:  70  f-value:  13.44534  pgrad:  11.99571 
iter:  80  f-value:  11.40815  pgrad:  1.799464 
iter:  90  f-value:  9.712975  pgrad:  4.29862 
iter:  100  f-value:  8.392164  pgrad:  11.32991 
iter:  110  f-value:  7.311477  pgrad:  1.565696 
iter:  120  f-value:  6.639707  pgrad:  3.421991 
iter:  130  f-value:  6.193688  pgrad:  22.20667 
iter:  140  f-value:  4.66529  pgrad:  1.574616 
iter:  150  f-value:  3.937451  pgrad:  8.75098 
iter:  160  f-value:  3.153241  pgrad:  6.673114 
iter:  170  f-value:  2.208422  pgrad:  1.53933 
iter:  180  f-value:  1.669985  pgrad:  0.8507576 
iter:  190  f-value:  1.449601  pgrad:  1.953953 
iter:  200  f-value:  1.371948  pgrad:  0.6711463 
iter:  210  f-value:  1.114267  pgrad:  1.776885 
iter:  220  f-value:  0.9583621  pgrad:  1.568243 
iter:  230  f-value:  0.8269146  pgrad:  3.633741 
iter:  240  f-value:  0.6304826  pgrad:  0.3339276 
iter:  250  f-value:  0.5107885  pgrad:  0.2684569 
iter:  260  f-value:  0.4613847  pgrad:  0.2476938 
iter:  270  f-value:  0.3270633  pgrad:  11.01763 
iter:  280  f-value:  0.1742687  pgrad:  0.444439 
iter:  290  f-value:  0.1625566  pgrad:  0.1235645 
iter:  300  f-value:  0.101921  pgrad:  1.459339 
iter:  310  f-value:  0.09256554  pgrad:  0.08955312 
iter:  320  f-value:  0.04521948  pgrad:  0.05963155 
iter:  330  f-value:  0.02634377  pgrad:  0.04566414 
iter:  340  f-value:  0.01193873  pgrad:  0.0904557 
iter:  350  f-value:  0.008038826  pgrad:  0.1842721 
iter:  360  f-value:  0.01248124  pgrad:  3.643765 
iter:  370  f-value:  0.001487418  pgrad:  0.1724186 
iter:  380  f-value:  0.0009728912  pgrad:  0.008121104 
iter:  390  f-value:  0.0001587139  pgrad:  0.003207078 
iter:  400  f-value:  1.091916e-07  pgrad:  4.596227e-05 
  Successful convergence.
$par
 [1] 0.9999292 0.9998582 0.9999353 0.9998704 0.9999426 0.9998850 0.9999344
 [8] 0.9998686 0.9999350 0.9998698 0.9999351 0.9998700 0.9999316 0.9998630
[15] 0.9999404 0.9998806 0.9999350 0.9998699 0.9999125 0.9998247 0.9999356
[22] 0.9998711 0.9999310 0.9998619 0.9999353 0.9998704 0.9999356 0.9998710
[29] 0.9999353 0.9998705 0.9999378 0.9998755 0.9999341 0.9998680 0.9999349
[36] 0.9998695 0.9999350 0.9998697 0.9999347 0.9998693 0.9999360 0.9998718
[43] 0.9999330 0.9998659 0.9999348 0.9998694 0.9999351 0.9998700 0.9999344
[50] 0.9998686

$value
[1] 1.091439e-07

$gradient
[1] 4.597844e-05

$fn.reduction
[1] 10824.77

$iter
[1] 401

$feval
[1] 493

$convergence
[1] 0

$message
[1] "Successful convergence"

$cpar
method      M 
     3     10 

BB documentation built on May 30, 2017, 2:49 a.m.