Using convex continuous piecewise linear function for the optimization of storage

First let us load the package

library(ConConPiWiFun)

## Warning: package 'Rcpp' was built under R version 2.15.3

Now we create the cost functions \( C_i \) \( i=1,\dots,n \). These are

CCPWLfuncList=new(cplfunctionvec) 
n=1000; Y=rnorm(n); 
S1=array(-1,n); S2=array(1,n); ## increasing slopes -1, 1 for all C_i i=1,..,n
B0=array(-Inf,n); B1=rnorm(n); ## increasing breakpoints -Inf, N(0,1) for all C_i i=1,..,n
CCPWLfuncList$SerialPush_2Breaks_Functions(S1,S2,B0,B1);

Then, we define the constraints on storage (capacity and power constraints)

Pmoins = array(-1, n)
Pplus = array(1, n)
Cmoins = array(0, n)
Cplus = array(5, n)

and perform the optimization:

res = CCPWLfuncList$OptimMargInt(Pmoins, Pplus, Cmoins, Cplus)