R: e04mf: LP problem (dense)

e04mf {NAGFWrappers}

R Documentation

e04mf: LP problem (dense)

Description

e04mf solves general linear programming problems. It is not intended for large sparse problems.

Usage

e04mf(a, bl, bu, cvec, istate, x, optlist,
      n = nrow(x),
      nclin = nrow(a))

Arguments

a

double array

The ith row of a must contain the coefficients of the ith general linear constraint for i=1 . . . m_L.

bl

double array

bu

double array

Must contain the lower bounds and bu the upper bounds, for all the constraints in the following order. The first n elements of each array must contain the bounds on the variables, and the next m_L elements the bounds for the general linear constraints (if any). To specify a nonexistent lower bound (i.e., l_j = - infinity), set bl[j] <= - bigbnd, and to specify a nonexistent upper bound (i.e., u_j = + infinity), set bu[j] >= bigbnd; the default value of bigbnd is 10^20, but this may be changed by the optional argument infiniteboundsize. To specify the jth constraint as an equality, set bl[j] = bu[j] = β, say, where abs(β) < bigbnd.

cvec

double array

The coefficients of the objective function when the problem is of type LP.

istate

integer array

Need not be set if the (default) optional argument coldstart is used.

x

double array

An initial estimate of the solution.

optlist

options list

Optional parameters may be listed, as shown in the following table:

Name	Type	Default
`Check Frequency`	integer	Default = 50
`Cold Start`		Default
`Warm Start`
`Crash Tolerance`	double	Default = 0.01
`Defaults`
`Expand Frequency`	integer	Default = 5
`Feasibility Tolerance`	double	Default = sqrt(ε)
`Infinite Bound Size`	double	Default = 10^20
`Infinite Step Size`	double	Default = max(bigbnd, 10^20)
`Iteration Limit`	integer	Default = max(50, 5(n + m_L))
`Iters`
`Itns`
`List`		Default for e04mf = list
`Nolist`		Default for e04mf = nolist
`Minimum Sum of Infeasibilities`	no	Default = NO
`Monitoring File`	integer	Default = - 1
`Optimality Tolerance`	double	Default = ε^0.8
`Print Level`	integer	= 0
`Problem Type`	string	Default = LP

n

integer: default = nrow(x)

, the number of variables.

nclin

integer: default = nrow(a)

m_L

, the number of general linear constraints.

Details

R interface to the NAG Fortran routine E04MFF.

Value

`ISTATE`	integer array The status of the constraints in the working set at the point returned in x. The significance of each possible value of istate[j] is as follows:
`X`	double array The point at which e04mf terminated. If ifail =0, ifail =1, ifail =4, x contains an estimate of the solution.
`ITER`	integer The total number of iterations performed.
`OBJ`	double The value of the objective function at x if x is feasible, or the sum of infeasibiliites at x otherwise. If the problem is of type FP and x is feasible, obj is set to zero.
`AX`	double array The final values of the linear constraints Ax.
`CLAMDA`	double array The values of the Lagrange multipliers for each constraint with respect to the current working set. The first n elements contain the multipliers for the bound constraints on the variables, and the next m_L elements contain the multipliers for the general linear constraints (if any). If istate[j] = 0 (i.e., constraint j is not in the working set), clamda[j] is zero. If x is optimal, clamda[j] should be non-negative if istate[j] = 1, non-positive if istate[j] = 2 and zero if istate[j] = 4.
`IFAIL`	integer ifail =0 unless the function detects an error or a warning has been flagged (see the Errors section in Fortran library documentation).

Author(s)

NAG

References

http://www.nag.co.uk/numeric/FL/nagdoc_fl23/pdf/E04/e04mff.pdf

Examples


optlist<-list()

ifail<-0

a<-matrix(c(1,1,1,1,1,1,1,0.15,0.04,0.02,0.04,0.02,0.01,0.03,0.03,0.05,0.08,0.02,0.06,0.01,0,0.02,0.04,0.01,0.02,0.02,0,0,0.02,0.03,0,0,0.01,0,0,0.7,0.75,0.8,0.75,0.8,0.97,0,0.02,0.06,0.08,0.12,0.02,0.01,0.97),nrow=7,ncol=7,byrow=TRUE)



bl<-matrix(c(-0.01,-0.1,-0.01,-0.04,-0.1,-0.01,-0.01,-0.13,-9.999999999999999e+24,-9.999999999999999e+24,-9.999999999999999e+24,-9.999999999999999e+24,-0.0992,-0.003),nrow=14,ncol=1,byrow=TRUE)



bu<-matrix(c(0.01,0.15,0.03,0.02,0.05,9.999999999999999e+24,9.999999999999999e+24,-0.13,-0.004900000000000001,-0.0064,-0.0037,-0.0012,9.999999999999999e+24,0.002),nrow=14,ncol=1,byrow=TRUE)



cvec<-matrix(c(-0.02,-0.2,-0.2,-0.2,-0.2,0.04,0.04),nrow=7,ncol=1,byrow=TRUE)



istate<-as.matrix(mat.or.vec(14,1))

x<-matrix(c(-0.01,-0.03,0,-0.01,-0.1,0.02,0.01),nrow=7,ncol=1,byrow=TRUE)



e04mf(a,bl,bu,cvec,istate,x,optlist)

[Package NAGFWrappers version 24.0 Index]