R: e04nc: Convex QP problem or linearly-constrained linear least...

e04nc {NAGFWrappers}

R Documentation

e04nc: Convex QP problem or linearly-constrained linear least squares problem (dense)

Description

e04nc solves linearly constrained linear least squares problems and convex quadratic programming problems. It is not intended for large sparse problems.

Usage

e04nc(c, bl, bu, cvec, istate, kx, x, a, b, optlist,
      m = nrow(a),
      n = nrow(kx),
      nclin = nrow(c))

Arguments

c

double array

The ith row of c must contain the coefficients of the ith general constraint for i=1 . . . nclin.

bl

double array

bu

double array

Bl 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 n_L elements must contain 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 bu[j] = bl[j] = β, say, where abs(β) < bigbnd.

cvec

double array

The coefficients of the explicit linear term of the objective function.

istate

integer array

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

kx

integer array

Need not be initialized for problems of type FP, LP, QP1, QP2, LS1 (the default) or LS2.

x

double array

An initial estimate of the solution.

a

double array

The array a must contain the matrix A as specified in table1 (see the Description in Fortran library documentation).

b

double array

The m elements of the vector of observations.

optlist

options list

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

Name	Type	Default
`Cold Start`		Default
`Warm Start`
`Crash Tolerance`	double	Default = 0.01
`Defaults`
`Feasibility Phase Iteration Limit`	integer	Default = max(50, 5(n + n_L))
`Optimality Phase Iteration Limit`	integer	Default = max(50, 5(n + n_L))
`Feasibility Tolerance`	double	Default = sqrt(ε)
`Hessian`	no	Default = NO
`Infinite Bound Size`	double	Default = 10^20
`Infinite Step Size`	double	Default = max(bigbnd, 10^20)
`Iteration Limit`	integer	Default = max(50, 5(n + n_L))
`Iters`
`Itns`
`List`		Default for e04nc = list
`Nolist`		Default for e04nc = nolist
`Monitoring File`	integer	Default = - 1
`Print Level`	integer	= 0
`Problem Type`	string	Default = LS1
`Rank Tolerance`	double	Default = 100ε or 10sqrt(ε) (see below)

m

integer: default = nrow(a)

, the number of rows in the matrix A. If the problem is specified as type FP or LP, m is not referenced and is assumed to be zero.

n

integer: default = nrow(kx)

, the number of variables.

nclin

integer: default = nrow(c)

n_L

, the number of general linear constraints.

Details

R interface to the NAG Fortran routine E04NCF.

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:
`KX`	integer array Defines the order of the columns of a with respect to the ordering of x, as described above.
`X`	double array The point at which e04nc terminated. If ifail =0, ifail =1, ifail =4, x contains an estimate of the solution.
`A`	double array If hessian=NO and the problem is of type LS or QP, a contains the upper triangular Cholesky factor R of eqn8 (see the Fortran library documentation), with columns ordered as indicated by kx. If hessian=YES and the problem is of type LS or QP, a contains the upper triangular Cholesky factor R of the Hessian matrix H, with columns ordered as indicated by kx. In either case R may be used to obtain the variance-covariance matrix or to recover the upper triangular factor of the original least squares matrix.
`B`	double array The transformed residual vector of equation eqn10 (see the Fortran library documentation).
`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.
`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 n_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/e04ncf.pdf

Examples


optlist<-list()

ifail<-0

c<-matrix(c(1,1,1,1,1,1,1,1,4,1,2,3,4,-2,1,1,1,1,1,-1,1,-1,1,1,1,1,1),nrow=3,ncol=9,byrow=TRUE)



bl<-matrix(c(0,0,-9.999999999999999e+24,0,0,0,0,0,0,2,-9.999999999999999e+24,1),nrow=12,ncol=1,byrow=TRUE)



bu<-matrix(c(2,2,2,2,2,2,2,2,2,9.999999999999999e+24,2,4),nrow=12,ncol=1,byrow=TRUE)



cvec<-matrix(c(0),nrow=1,ncol=1,byrow=TRUE)



istate<-as.matrix(mat.or.vec(12,1))

kx<-as.matrix(mat.or.vec(9,1))

x<-matrix(c(1,0.5,0.3333,0.25,0.2,0.1667,0.1428,0.125,0.1111),nrow=9,ncol=1,byrow=TRUE)



a<-matrix(c(1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,0,0,1,1,3,1,1,1,-1,-1,-3,1,1,1,4,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,2,1,1,0,0,0,-1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,2,2,3,1,0,1,1,1,1,0,2,2),nrow=10,ncol=9,byrow=TRUE)



b<-matrix(c(1,1,1,1,1,1,1,1,1,1),nrow=10,ncol=1,byrow=TRUE)



e04nc(c,bl,bu,cvec,istate,kx,x,a,b,optlist)

[Package NAGFWrappers version 24.0 Index]