quadcon: Quadratic Constraint
In optiSolve: Linear, Quadratic, and Rational Optimization

Description Usage Arguments Details Value See Also Examples

Define a quadratic constraint of the form

x' Q x + a' x + d <= val

1 2	quadcon(Q, a=rep(0, nrow(Q)), d=0, dir="<=", val, id=1:nrow(Q), name="quadratic", use=TRUE)

`Q`	Numeric symmetric matrix of the constraint coefficients.
`a`	Numeric vector.
`d`	Numeric value.
`dir`	Character string `"<="`.
`val`	Numeric threshold value, which is the upper bound for the quadratic function.
`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.
`name`	Name for the constraint.
`use`	Logical value indicating if the constraint should be included in the optimization problem. If `use=FALSE`, then constraint does not affect the result, but the value of the quadratic function will be reported by function validate.

Define a quadratic inequality constraint of the form

x' Q x + a' x + d <= val.

Vector x contains only the variables included in argument id.

An object of class quadCon.

The main function for solving constrained programming problems is solvecop.

### 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       ###

data(phenotype)
data(myQ)

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

mycop <- cop(f  = linfun(a=phenotype$BV, id=phenotype$Indiv, name="BV"),
             max= TRUE,
             lb = lbcon(0,  id=phenotype$Indiv), 
             ub = ubcon(NA, id=phenotype$Indiv),
             lc = lincon(A=A, dir=dir, val=val, id=phenotype$Indiv),
             qc = quadcon(Q=myQ, d=0.001, val=0.035, name="Kinship", id=rownames(myQ)))

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

validate(mycop, res)

#            valid solver  status
#             TRUE  cccp2 optimal
#
#   Variable     Value      Bound    OK?
#   -------------------------------------
#   BV           0.7667 max        :      
#   -------------------------------------
#   lower bounds all x  >=  lb     : TRUE 
#   Sexfemale    0.5    ==  0.5    : TRUE 
#   Sexmale      0.5    ==  0.5    : TRUE 
#   Kinship      0.035  <=  0.035  : TRUE 
#   -------------------------------------