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# maxfn.R
## author: John C. Nash
# solution: 1:n has maximum of 10.
maxfn<-function(x) {# fn to be MAXIMIZED
# max = 10 at 1:n
n<-length(x)
ss<-seq(1,n)
f<-10-sum((x-ss)^2)
f
}
maxfn.g <- function(x) { # gradient
n <- length(x)
ss<-seq(1,n)
gg <- -2*(x-ss)
gg
}
maxfn.h <- function(x) { # gradient
n <- length(x)
hh<-rep(-2, n)
hh <- diag(hh)
hh
}
# solution: 1:n has minimum of -10.
negmaxfn<-function(x) {# explicit negative of maxfn
f<-(-1)*maxfn(x)
return(f)
}
negmaxfn.g<-function(x) {# explicit negative of maxfn
gg<-(-1)*maxfn.g(x)
gg
}
negmaxfn.h<-function(x) {# explicit negative of maxfn
hh<-(-1)*maxfn.h(x)
hh
}
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