var p;
var alpha;
var t_0;

param N;
param t{1..N};
param P{1..N};

var g{i in 1..N} = p/(1+exp(-alpha*(t[i]-t_0)));

minimize f: sum{i in 1..N} (P[i]-g[i])^2;

let p:= 500;
let t_0:= 2000;
let alpha:= 0.024;