Grid evaluation of a constrained or unconstrained cost function

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Description

Evaluate a constrained or unconstrained cost function on a grid of points around a given initial point estimate.

Usage

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  optimbase.gridsearch(fun = NULL, x0 = NULL, xmin = NULL, 
                       xmax = NULL, npts = 3, alpha = 10)

Arguments

fun

A constrained or unconstrained cost function defined as described in the vignette (vignette('optimbase',package='optimbase')).

x0

The initial point estimate, provided as a numeric vector.

xmin

Optional: a vector of lower bounds.

xmax

Optional: a vector of upper bounds.

npts

A integer scalar greater than 2, indicating the number of evaluation points will be used on each dimension to build the search grid.

alpha

A vector of numbers greater than 1, which give the factor(s) used to calculate the evaluation range of each dimension of the search grid (see Details). If alpha length is lower than that of x0, elements of alpha are recycled. If its length is higher than that of x0, alpha is truncated.

Details

optimbase.gridsearch evaluates the cost function at each point of a grid of npts^length(x0) points. If lower (xmin) and upper (xmax) bounds are provided, the range of evaluation points is limited by those bounds and alpha is not used. Otherwise, the range of evaluation points is defined as [x0/alpha,x0*alpha].

optimbase.gridsearch also determines if the cost function is feasible at each evaluation point by calling optimbase.isfeasible.

Value

Return a data.frame with the coordinates of the evaluation point, the value of the cost function and its feasibility. The data.frame is ordered by feasibility and increasing value of the cost function.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.isfeasible

Examples

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# Problem: find x and y that maximize 3.6*x - 0.4*x^2 + 1.6*y - 0.2*y^2 and
#          satisfy the constrains:
#            2*x - y <= 10
#            x >= 0
#            y >= 0
#

gridfun <- function(x=NULL,index=NULL,fmsfundata=NULL,...){

  f <- c()
  c <- c()
  if (index == 2 | index == 6)
    f <- -(3.6*x[1] - 0.4*x[1]*x[1] + 1.6*x[2] - 0.2*x[2]*x[2])
  if (index == 5 | index == 6)
    c <- c(10 - 2*x[1] - x[2],
           x[1],
           x[2])
  varargout <- list(f = f, g = c(), c = c, gc = c(), index = index)

  return(varargout)
}


x0 <- c(0.35,0.3)
npts <- 6
alpha <- 10

res <- optimbase.gridsearch(fun=gridfun,x0=x0,xmin=NULL,xmax=NULL,
                     npts=npts,alpha=alpha)

# 3.5 and 3 is the actual solution of the optimization problem
print(res)