BB: multiStart – R documentation

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multiStart

Nonlinear Optimization or Root-Finding with Multiple Starting Values

Description

Start BBsolve or BBoptim from multiple starting points to obtain multiple solutions and to test sensitivity to starting values.

Usage

multiStart(par, fn, gr=NULL, action = c("solve", "optimize"), 
	method=c(2,3,1),  lower=-Inf, upper=Inf,
	project=NULL, projectArgs=NULL, 
	control=list(),  quiet=FALSE, details=FALSE, ...)

Arguments

`par`	A real matrix, each row of which is an argument to `fn`, indicating initial guesses for solving a nonlinear system `fn = 0` or for optimizing the objective function `fn`.
`fn`	see `BBsolve` or `BBoptim`.
`gr`	Only required for optimization. See `BBoptim`.
`action`	A character string indicating whether to solve a nonlinear system or to optimize. Default is “solve”.
`method`	see `BBsolve` or `BBoptim`.
`upper`	An upper bound for box constraints. See `spg`
`lower`	An lower bound for box constraints. See `spg`
`project`	A projection function or character string indicating its name. 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`	A list with arguments to the `project` function.
`control`	See `BBsolve` and `BBoptim`.
`quiet`	A logical variable (TRUE/FALSE). If `TRUE` warnings and some additional information printing are suppressed. Default is `quiet = FALSE` Note that the `control` variable `trace` and `quiet` affect different printing, so if `trace` is not set to `FALSE` there will be considerable printed output.
`details`	Logical indicating if the result should include the full result from `BBsolve` or `BBoptim` for each starting value.
`...`	arguments passed fn (via the optimization algorithm).

Details

The optimization or root-finder is run with each row of par indicating initial guesses.

Value

list with elements par, values, and converged. It optionally returns an attribute called “details”, which is a list as long as the number of starting values, which contains the complete object returned by dfsane or spg for each starting value.

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/

Examples

# Use a preset seed so the example is reproducable. 
require("setRNG")
old.seed <- setRNG(list(kind="Mersenne-Twister", normal.kind="Inversion",
    seed=1234))

# Finding multiple roots of a nonlinear system
brownlin <- function(x) {
# Brown's almost linear system(A.P. Morgan, ACM 1983)
# two distinct solutions if n is even
# three distinct solutions if n is odd  
  	n <- length(x)
  	f <- rep(NA, n)
	nm1 <- 1:(n-1)
	f[nm1] <- x[nm1] + sum(x) - (n+1)
	f[n] <- prod(x) - 1 
	f
}

p <- 9
n <- 50
p0 <- matrix(rnorm(n*p), n, p)  # n starting values, each of length p
ans <- multiStart(par=p0, fn=brownlin)
pmat <- ans$par[ans$conv, 1:p] # selecting only converged solutions
ord1 <- order(abs(pmat[,1]))
round(pmat[ord1, ], 3)  # all 3 roots can be seen

# An optimization example
rosbkext <- function(x){
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)

pmat <- matrix(rnorm(100), 20, 5)  # 20 starting values each of length 5 
ans <- multiStart(par=pmat, fn=rosbkext, action="optimize")
ans
attr(ans, "details")[[1]]  # 

pmat <- ans$par[ans$conv, 1:5] # selecting only converged solutions
round(pmat, 3)

BB

Solving and Optimizing Large-Scale Nonlinear Systems

v2019.10-1

GPL-3

Authors

Ravi Varadhan [aut, cph, trl], Paul Gilbert [aut, cre], Marcos Raydan [ctb] (with co-authors, wrote original algorithms in fortran. These provided some guidance for implementing R code in the BB package.), JM Martinez [ctb] (with co-authors, wrote original algorithms in fortran. These provided some guidance for implementing R code in the BB package.), EG Birgin [ctb] (with co-authors, wrote original algorithms in fortran. These provided some guidance for implementing R code in the BB package.), W LaCruz [ctb] (with co-authors, wrote original algorithms in fortran. These provided some guidance for implementing R code in the BB package.)

Initial release