distsuml2min: distsuml2min at orloca package

In orloca: Operations Research LOCational Analysis Models

distsuml2min at orloca package

Description

distsuml2min is the distsummin function for the Euclidean norm (l_2). This function returns the solution of the minimization problem. Mainly for internal use.

Usage

distsuml2min(
  o,
  x = 0,
  y = 0,
  max.iter = 100,
  eps = 0.001,
  verbose = FALSE,
  algorithm = "Weiszfeld",
  ...
)

Arguments

o	An object of loca.p class.
x	The x coordinate of the starting point. It's default value is 0.
y	The y coordinate of the starting point. It's default value is 0.
max.iter	Maximum number of iterations allowed. It's default value is 100000.
eps	The module of the gradient in the stop rule. It's default value is 1e-3.
verbose	If TRUE the function produces detailed output. It's default value is FALSE.
algorithm	The method to be use. For this version of the package, the valid values are: "gradient" for a gradient based method, "search" for local search method (this option is deprecated), "ucminf" for optimization with ucminf from ucminf package, and "Weiszfeld" for the Weiszfeld method or any of the valid method for optim function, now "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN". "Weiszfeld" is the default value.

Details

The algorithms Weiszfeld and gradient include and optimality test for demand points. The Weiszfeld version of the algorithm also implements slow convergence test and accelerator procedure.

If p < 1 thus l_p is not a norm, so, only p \ge 1 are valid values.

Since l_2 norm is the Euclidean norm, when p=2 distsumlpmin are equal to distsummin. But the computations involved are greater for the first form.

max.iter for SANN algorithm is the number of evaluation of objective function, so this method usually requires large values of max.iter to reach optimal value

The function zsummin is deprecated and will be removed from new versions of the package.

Value

distsummin returns an array with the coordinates of the solution point.

See Also

See also orloca-package, loca.p and distsum.

Examples

# A new unweighted loca.p object
loca <- loca.p(x = c(-1, 1, 1, -1), y = c(-1, -1, 1, 1))
# Compute the minimum
sol<-distsummin(loca)

# Show the result
sol

# Evaluation of the objective function at solution point
distsum(loca, sol[1], sol[2])

orloca documentation built on Feb. 1, 2024, 3 p.m.