R Under development (unstable) (2023-10-23 r85401 ucrt) -- "Unsuffered Consequences"
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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
+ }
> 
> 
> proc.time()
   user  system elapsed 
   0.10    0.03    0.12