solvecop {optiSolve}

Solve a Constrained Optimization Problem

Description

Solve a constrained optimization problem with a linear, quadratic, or rational objective function, and linear, quadratic, rational, and boundary constraints.

Usage

solvecop(op, solver="default", make.definite=FALSE, X=NULL, quiet=FALSE, ...)

Arguments

op

An optimization problem, usually created with function cop.

solver

Character string with the name of the solver. Available solvers are "alabama", "cccp", "cccp2", and "slsqp". Solver "csdp" is temporarily disabled because the package Rcsdp has been removed from Cran. The default means that the solver is chosen automatically. The solvers are described in the Details section.

make.definite

Logical variable indicating whether non-positive-semidefinite matrices should be approximated by positive-definite matrices. This is always done for solvers that are known not to convergue otherwise.

X

Starting vector of parameter values (not needed). Any initial vector, even those violating linear inequality constraints, may be specified. Ignored by solvers "cccp" and "csdp". For "slsqp" the lower and upper bounds must not be violated.

quiet

Logical variable indicating whether output to console should be switched off.

...

Tuning parameters of the solver. The available parameters depend on the solver and will be printed when the function is used with quiet=FALSE. In section Details it is mentioned where descriptions of these parameters can be found.

Details

Solve a constrained optimization problem with a linear, quadratic, or rational objective function, and linear, quadratic, rational, and boundary constraints.

Solver

"alabama": The augmented lagrangian minimization algorithm auglag from package alabama is called. The method combines the objective function and a penalty for each constraint into a single function. This modified objective function is then passed to another optimization algorithm with no constraints. If the constraints are violated by the solution of this sub-problem, then the size of the penalties is increased and the process is repeated. The default methods for the uncontrained optimization in the inner loop is the quasi-Newton method called BFGS. Tuning parameters used for the outer loop are described in the details section of the help page of function auglag. Tuning parameters used for the inner loop are described in the details section of the help page of function optim.

"cccp" and "cccp2": Function cccp from package cccp for solving cone constrained convex programs is called. For solver "cccp", quadratic constraints are converted into second order cone constraints, which requires to approximate non-positive-semidefinite matrices by positive-definite matrices. For solver "cccp2", quadratic constraints are defined by functions. The implemented algorithms are partially ported from CVXOPT. Tuning parameters are those from function ctrl.

"slsqp": The sequential (least-squares) quadratic programming (SQP) algorithm slsqp for gradient-based optimization from package nloptr. The algorithm optimizes successive second-order (quadratic/least-squares) approximations of the objective function, with first-order (affine) approximations of the constraints. Available parameters are described in nl.opts

Value

A list with the following components:

x

Named numeric vector with parameters optimizing the objective function while satisfying constraints, if convergence is successful.

solver

Name of the solver used for optimization.

status

Message indicating type of convergence as reported by the solver.

Author(s)

Robin Wellmann

Examples

### Quadratic programming with linear constraints      ###
### Example from animal breeding                       ###
### where the mean kinship in the offspring is minized ###

data(phenotype)
data(myQ)

A   <- t(model.matrix(~Sex+BV-1, data=phenotype))
rownames(A) <- c("male.cont","female.cont", "Breeding.Value")
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, trace=FALSE)

head(res$x)

hist(res$x,breaks=50,xlim=c(0,0.5))

Evaluation <- validate(mycop, res)

Evaluation$summary

Evaluation$info

Evaluation$obj.fun

Evaluation$var

Evaluation$var$Breeding.Value