param x_I;
param y_I;
param x_F;
param y_F;
param N;

var x{1..N};
var y{1..N};

minimize f: sum {i in 1..N} y[i];
s.t. g_1: x[1]= x_I;
     g_2: y[1]= y_I;
     g_3: x[N]= x_F;
     g_4: y[N]= y_F;
     g_5 {i in 1..(N-1)}: (x[i+1]-x[i])^2 + (y[i+1]-y[i])^2 <= 1;