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# objective function for penalty multiplier estimation
fopt_groups <- function(par, lambda2, nparts, partsind, partsmat, sizes, G,
sum1) {
s <- par[1]
loglambdag <- par[-1]
loglambdasum <- rowSums(sapply(1:nparts, function(part) {
loglambdag[partsind==part][partsmat[, part]]}))
partsum <- sum((0.5*lambda2*unlist(sapply(1:nparts, function(part) {
tapply(exp(loglambdasum)*sum1, partsmat[, part], sum)})) + (s - 0.5)*sizes)^2)
constr <- sum(loglambdag*sizes)^2
magn <- partsum + constr
return(magn)
}
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