ratiofun {optiSolve}

Rational Objective Function

Description

Define a rational objective function of the form

f(x) = \frac{x^T Q_1 x + a_1 x + d_1}{x^T Q_2 x + a_2 x + d_2}

Usage

ratiofun(Q1, a1=rep(0, nrow(Q1)), d1=0, Q2, a2=rep(0, nrow(Q2)), d2=0, 
   id=1:nrow(Q1), name="ratio.fun")

Arguments

Q1

Numeric quadratic matrix.

a1

Numeric vector.

d1

Numeric value.

Q2

Numeric quadratic matrix.

a2

Numeric vector.

d2

Numeric value.

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.

Details

Define a rational ofjective function of the form

f(x) = \frac{x^T Q_1 x + a_1 x + d_1}{x^T Q_2 x + a_2 x + d_2}

Reasonable bounds for the variables should be provided because the function can have several local optima. Solvers 'slsqp' (the default) and 'alabama' are recommended.

Value

An object of class ratioFun.

See Also

The main function for solving constrained programming problems is solvecop.

Examples

### Constrained optimization with rational objective                  ### 
### function and linear and quadratic constraints                     ###
### Example from animal breeding                                      ###
### The mean kinship at native alleles in the offspring is minimized  ###
### The mean breeding value and the mean kinship are constrained      ###

data(phenotype)
data(myQ)
data(myQ1)
data(myQ2)

Ax <- t(model.matrix(~Sex+BV+MC-1, data=phenotype))
Ax[,1:5]
val <- c(0.5,  0.5,  0.4,  0.5 )
dir <- c("==", "==", ">=", "<=")

mycop <- cop(f  = ratiofun(Q1=myQ1, Q2=myQ2, d1=0.0004, d2=0.00025, 
                           id=rownames(myQ1), name="nativeKinship"),
             lb = lbcon(0,  id=phenotype$Indiv), 
             ub = ubcon(NA, id=phenotype$Indiv),
             lc = lincon(A=Ax, 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, quiet=FALSE)

validate(mycop, res)

#            valid solver                status
#             TRUE  slsqp successful completion
#
#   Variable      Value      Bound    OK?
#   --------------------------------------
#   nativeKinship 0.0366 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 
#   MC            0.4963 <=  0.5    : TRUE 
#   Kinship       0.035  <=  0.035  : TRUE 
#   --------------------------------------