lbfgsb3c (version 2020-3.2)

lbfgsb3c: Interfacing wrapper for the Nocedal - Morales LBFGSB3 (Fortran) limited memory BFGS solver.

Description

Interfacing wrapper for the Nocedal - Morales LBFGSB3 (Fortran) limited memory BFGS solver.

Usage

lbfgsb3c(
  par,
  fn,
  gr = NULL,
  lower = -Inf,
  upper = Inf,
  control = list(),
  ...,
  rho = NULL
)
lbfgsb3(
  par,
  fn,
  gr = NULL,
  lower = -Inf,
  upper = Inf,
  control = list(),
  ...,
  rho = NULL
)
lbfgsb3f(
  par,
  fn,
  gr = NULL,
  lower = -Inf,
  upper = Inf,
  control = list(),
  ...,
  rho = NULL
)
lbfgsb3x(
  par,
  fn,
  gr = NULL,
  lower = -Inf,
  upper = Inf,
  control = list(),
  ...,
  rho = NULL
)

Value

A list of the following items

• par The best set of parameters found.

• value The value of fn corresponding to par.

• counts A two-element integer vector giving the number of calls to fn and gr respectively. This excludes any calls to fn to compute a finite-difference approximation to the gradient.

• convergence An integer code. 0 indicates successful completion

Arguments

par

A parameter vector which gives the initial guesses to the parameters that will minimize fn. This can be named, for example, we could use par=c(b1=1, b2=2.345, b3=0.123)

fn

A function that evaluates the objective function to be minimized. This can be a R function or a Rcpp function pointer.

gr

If present, a function that evaluates the gradient vector for the objective function at the given parameters computing the elements of the sum of squares function at the set of parameters start. This can be a R function or a Rcpp function pointer.

lower

Lower bounds on the parameters. If a single number, this will be applied to all parameters. Default -Inf.

upper

Upper bounds on the parameters. If a single number, this will be applied to all parameters. Default Inf.

control

An optional list of control settings. See below in details.

...

Any data needed for computation of the objective function and gradient.

rho

An Environment to use for function evaluation. If present the arguments in ... are ignored. Otherwise the ... are converted to an environment for evaluation.

Author

Matthew Fidler (move to C and add more options for adjustments), John C Nash <[e-mail]> (of the wrapper and edits to Fortran code to allow R output) Ciyou Zhu, Richard Byrd, Jorge Nocedal, Jose Luis Morales (original Fortran packages)

Details

See the notes below for a general appreciation of this package.

The control list can contain:

• trace If positive, tracing information on the progress of the optimization is produced. Higher values may produce more tracing information: for method "L-BFGS-B" there are six levels of tracing. (To understand exactly what these do see the source code: higher levels give more detail.)

• factr controls the convergence of the "L-BFGS-B" method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e7, that is a tolerance of about 1e-8.

• pgtol helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed.

• abstol helps control the convergence of the "L-BFGS-B" method. It is an absolute tolerance difference in x values. This defaults to zero, when the check is suppressed.

• reltol helps control the convergence of the "L-BFGS-B" method. It is an relative tolerance difference in x values. This defaults to zero, when the check is suppressed.

• lmm is an integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 5.

• maxit maximum number of iterations.

• iprint Provided only for compatibility with older codes. This control is no longer active.)

• info a boolean to indicate if more optimization information is captured and output in a $info list

References

Morales, J. L.; Nocedal, J. (2011). "Remark on 'algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization' ". ACM Transactions on Mathematical Software 38: 1.

Byrd, R. H.; Lu, P.; Nocedal, J.; Zhu, C. (1995). "A Limited Memory Algorithm for Bound Constrained Optimization". SIAM J. Sci. Comput. 16 (5): 1190-1208.

Zhu, C.; Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge (1997). "L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization". ACM Transactions on Mathematical Software 23 (4): 550-560.

See Also

Packages optim and optimx.

Examples

# Rosenbrock's banana function
n=3; p=100

fr = function(x)
{
    f=1.0
    for(i in 2:n) {
        f=f+p*(x[i]-x[i-1]**2)**2+(1.0-x[i])**2
    }
    f
}

grr = function(x)
{
    g = double(n)
    g[1]=-4.0*p*(x[2]-x[1]**2)*x[1]
    if(n>2) {
        for(i in 2:(n-1)) {
            g[i]=2.0*p*(x[i]-x[i-1]**2)-4.0*p*(x[i+1]-x[i]**2)*x[i]-2.0*(1.0-x[i])
        }
    }
    g[n]=2.0*p*(x[n]-x[n-1]**2)-2.0*(1.0-x[n])
    g
}
x = c(a=1.02, b=1.02, c=1.02)
(opc <- lbfgsb3c(x,fr, grr))
(op <- lbfgsb3(x,fr, grr, control=list(trace=1)))
(opx <- lbfgsb3x(x,fr, grr))
(opf <- lbfgsb3f(x,fr, grr))