quadfun {optiSolve}

Quadratic Objective Function

Description

Define a quadratic objective function of the form

f(x) = x^T Qx + a^T x + d

Usage

quadfun(Q, a=rep(0, nrow(Q)), d=0, id=1:nrow(Q), name="quad.fun")

Arguments

Q

Numeric symmetric matrix of the constraint coefficients.

a

Numeric vector.

d

Numeric value.

id

Vector (if present), defining the names of the variables to which the function applies. Each variable name corresponds to one component of x. Variable names must be consistent across constraints.

name

Name for the objective function.

Details

Define a quadratic objective function of the form

f(x) = x^T Qx + a^T x + d

Value

An object of class quadFun.

See Also

The main function for solving constrained programming problems is solvecop.

Examples

### Quadratic programming with linear constraints       ###
### Example from animal breeding                        ###
### The mean kinship in the offspring x'Qx+d is minized ###
### and the mean breeding value is restricted.          ###

data(phenotype)
data(myQ)

A   <- t(model.matrix(~Sex+BV-1, data=phenotype))
A[,1:5]
val <- c(0.5, 0.5, 0.40)
dir <- c("==","==",">=")

mycop <- cop(f  = quadfun(Q=myQ, d=0.001, name="Kinship", id=rownames(myQ)), 
             lb = lbcon(0,  id=phenotype$Indiv), 
             ub = ubcon(NA, id=phenotype$Indiv),
             lc = lincon(A=A, dir=dir, val=val, id=phenotype$Indiv))

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

validate(mycop, res)

#            valid solver  status
#             TRUE   cccp optimal
#
#   Variable     Value      Bound    OK?
#   -------------------------------------
#   Kinship      0.0322 min        :      
#   -------------------------------------
#   lower bounds all x  >=  lb     : TRUE 
#   Sexfemale    0.5    ==  0.5    : TRUE 
#   Sexmale      0.5    ==  0.5    : TRUE 
#   BV           0.4    >=  0.4    : TRUE 
#   -------------------------------------