lbcon {optiSolve}

Lower Bounds

Description

Define lower bounds for the variables of the form

val <= x.

Usage

lbcon(val=numeric(0), id=seq_along(val))

Arguments

val

Numeric vector with lower bounds for the variables. If val is a single value, then this value will be used for all variables in vector id.

id

Vector defining the names of the variables to which the constraint applies. Each variable name corresponds to one component of x. Variable names must be consistent across constraints.

Details

Define lower bounds for the variables of the form

val <= x.

Vector x contains only the variables included in argument id.

Value

An object of class lbCon.

See Also

The main function for solving constrained programming problems is solvecop.

Examples

### Linear programming with linear and quadratic constraints ###
### Example from animal breeding                             ###
### The mean breeding value BV is maximized whereas the      ###
### mean kinship in the offspring x'Qx+d is restricted       ###
### Lower and upper bounds for females are identical, so     ###
### their contributions are not optimized.                   ###
### Lower and upper bounds for some males are defined.       ###

data(phenotype)
data(myQ)

A   <- t(model.matrix(~Sex-1, data=phenotype))
A[,1:5]
val <- c(0.5,  0.5)
dir <- c("==","==")
Nf  <- sum(phenotype$Sex=="female")
id  <- phenotype$Indiv

lbval <- setNames(rep(0,  length(id)), id)
ubval <- setNames(rep(NA, length(id)), id)
lbval[phenotype$Sex=="female"] <- 1/(2*Nf)
ubval[phenotype$Sex=="female"] <- 1/(2*Nf)
lbval["276000102379430"] <- 0.02
ubval["276000121507437"] <- 0.03

mycop <- cop(f  = linfun(a=phenotype$BV, id=id, name="BV"),
             max= TRUE,
             lb = lbcon(lbval, id=id), 
             ub = ubcon(ubval, id=id),
             lc = lincon(A=A, dir=dir, val=val, id=id),
             qc = quadcon(Q=myQ, d=0.001, val=0.045, 
                          name="Kinship", id=rownames(myQ)))

res <- solvecop(mycop, solver="cccp2", quiet=FALSE)

Evaluation <- validate(mycop, res)

#            valid solver  status
#             TRUE  cccp2 optimal
#
#   Variable     Value      Bound    OK?
#   -------------------------------------
#   BV           0.5502 max        :      
#   -------------------------------------
#   lower bounds all x  >=  lb     : TRUE 
#   upper bounds all x  <=  ub     : TRUE 
#   Sexfemale    0.5    ==  0.5    : TRUE 
#   Sexmale      0.5    ==  0.5    : TRUE 
#   Kinship      0.045  <=  0.045  : TRUE 
#   -------------------------------------

res$x["276000102379430"]

res$x["276000121507437"]