I would like to write a piecewise constraint for an Abstract Model in Pyomo.
$$\operatorname{pu}_i(t_i^{'v})=\begin{align}\begin{cases}\rho_1(e_i'-t_i^{'v})+\rho_2(e_i-e_i'),\quad& t_i^{'v}\le e_i',\\\rho_2(e_i-t_i^{'v}),&e_i'<t_i^{'v}\le e_i,\\0,&e_i<t_i^{'v}\le l_i,\\\rho_3(t_i^{'v}-l_i),&l_i<t_i^{'v}\le l_i',\\\rho_3(l_i'-l_i)+\rho_4(t_i^{'v}-l_i'),&l_i'<t_i^{'v}.\end{cases}\end{align}$$
The only variable here is $t'^{v}_i$, the $\rho$, $e$, and $l$ values are defined in a separate .dat file.
Here is what I tried to do, but I am struggling with the breakpoints:
def PenaltyCost_rule(model, v, i):
if value(model.t[v,i]) <= model.ep[i]:
return model.pn[v,i] == model.rho[1]*(model.ep[i]-model.t[v,i]) + model.rho[2]*(model.e[i]-model.ep[i])
if value(model.t[v,i]) >= model.ep[i] & value(model.t[v,i])<= model.e[i]:
return model.pn[v,i] == model.rho[2]*(model.e[i]-model.t[v,i])
if value(model.t[v,i]) >= model.e[i] & value(model.t[v,i]) <= model.l[i]:
return model.pn[v,i] == 0
if value(model.t[v,i]) >= model.l[i] & value(model.t[v,i])<= model.lp[i]:
return model.pn[v,i] == model.rho[3]*(model.t[v,i]-model.l[i])
if value(model.t[v,i]) >= model.lp[i]:
return model.pn[v,i] == model.rho[1]*(model.ep[i]-model.tp[i,v]) + model.rho[3]*(model.t[i]-model.l[i])
model.PenaltyConstConstraint = Constraint(model.v, model.n, rule=PenaltyCost_rule)
bpts = [model.ep[i],model.e[i], model.l[i],model.lp[i]]
model.Penalty_constraint = Piecewise(
model.v, model.n,
model.t, model.pn,
pw_pts=bpts,
pw_repn='INC',
pw_constr_type = 'EQ',
f_rule = PenaltyCost_rule)
