ratiocon {optiSolve}

Rational Constraint

Description

Define a rational constraint of the form

\frac{x^T Q_1 x + a_1^T x + d_1}{x^T Q_2 x + a_2^T x + d_2} \leq val

Usage

ratiocon(Q1, a1=rep(0, nrow(Q1)), d1=0, Q2, a2=rep(0, nrow(Q2)), d2=0, dir="<=", val, 
   id=1:nrow(Q1), name="rational", use=TRUE)

Arguments

Q1

Numeric quadratic matrix.

a1

Numeric vector.

d1

Numeric value.

Q2

Numeric quadratic matrix.

a2

Numeric vector.

d2

Numeric value.

dir

Character string "<=".

val

Numeric threshold value, which is the upper bound for the rational 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 the constraint does not affect the result, but the value of the rational function will be reported by function validate.

Details

Define a rational inequality constraint of the form

\frac{x^T Q_1 x + a_1^T x + d_1}{x^T Q_2 x + a_2^T x + d_2} \leq val.

Vector x contains only the variables included in argument id.

For rational constraints it is required that there is a linear constraint ensuring that sum(x) is a constant. Furthermore, the denominator must be non-negative.

Value

An object of class ratioCon.

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)

A <- t(model.matrix(~Sex+BV+MC-1, data=phenotype))
A[,1:5]
val <- c(0.5,  0.5,  0.4,  0.5 )
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),
             rc = ratiocon(Q1=myQ1, Q2=myQ2, d1=0.0004, d2=0.00025, val=0.040, 
                           id=rownames(myQ1), name="nativeKinship")
             )

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

validate(mycop, res)

#            valid solver                status
#             TRUE  slsqp successful completion
#
#   Variable      Value      Bound    OK?
#   --------------------------------------
#   Kinship       0.0324 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            0.4668 <=  0.5    : TRUE 
#   nativeKinship 0.04   <=  0.04   : TRUE 
#   --------------------------------------