minimize.nonneg.cg {nonneg.cg}

Non-Negative CG Minimizer

Description

Minimize a differentiable function subject to all the variables being non-negative (i.e. >= 0), using a Conjugate-Gradient algorithm based on a modified Polak-Ribiere-Polyak formula (see reference at the bottom for details).

Usage

minimize.nonneg.cg(evaluate_function, evaluate_gradient, x0, tol = 1e-04,
  maxnfeval = 1500, maxiter = 200, decr_lnsrch = 0.5,
  lnsrch_const = 0.01, max_ls = 20, extra_nonneg_tol = FALSE,
  nthreads = 1, verbose = FALSE, ...)

Arguments

evaluate_function

function(x, ...) objective evaluation function

evaluate_gradient

function(x, ...) gradient evaluation function

x0

Starting point. Must be a feasible point (>=0). Be aware that it might be modified in-place.

tol

Tolerance for <gradient, direction>

maxnfeval

Maximum number of function evaluations

maxiter

Maximum number of CG iterations

decr_lnsrch

Number by which to decrease the step size after each unsuccessful line search

lnsrch_const

Acceptance parameter for the line search procedure

max_ls

Maximum number of line search trials per iteration

extra_nonneg_tol

Ensure extra non-negative tolerance by explicitly setting elements that are <=0 to zero at each iteration

nthreads

Number of parallel threads to use (ignored if the package was installed from CRAN)

verbose

Whether to print convergence messages

...

Extra parameters to pass to the objective and gradient functions

Details

The underlying C function can also be called directly from Rcpp with 'R_GetCCallable' (see example of such usage in the source code of the 'zoo' package).

References

Li, C. (2013). A conjugate gradient type method for the nonnegative constraints optimization problems. Journal of Applied Mathematics, 2013.

Examples

fr <- function(x) {   ## Rosenbrock Banana function
  x1 <- x[1]
  x2 <- x[2]
  100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
grr <- function(x) { ## Gradient of 'fr'
  x1 <- x[1]
  x2 <- x[2]
  c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1),
    200 *      (x2 - x1 * x1))
}
minimize.nonneg.cg(fr, grr, x0 = c(0,2), verbose=TRUE, tol=1e-8)