OR-Tools: Nonlinear constraints?

Question

I have inherited a reasonably simple ortools-based optimizer (Python) with linear relationships that I need to non-linear-ize, and I have no idea how to do that.

The relevant part of my problem looks like this:

solver = pywraplp.Solver("B", pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
...
# charging a battery
## cap_prev: capacity before the current timeslot
## cap: ditto afterwards
## b_chg: charging power
## all are NumVar(0,some_hardware_limit)

solver.Add(cap_prev + 0.9 * b_chg - b_dis == cap)

The problem is that I need to replace the 0.9 with something that depends on the value of b_chg. The Naïve solution looks like this:

solver.Add(cap_prev + b_chg_eff - b_dis == cap)

solver.Add(b_chg_eff == b_chg * (0.1+b_chg*0.8)).OnlyEnforceIf(b_chg<100)
solver.Add(b_chg_eff == b_chg * (0.9).OnlyEnforceIf(100<=b_chg<200)
solver.Add(b_chg_eff == b_chg * (0.9-(b_chg-200)*0.01).OnlyEnforceIf(200<=b_chg)

except that this is no longer linear, which kindof points to the assumption that I need a different solver.

Answer 1

If you are looking to linearize the 3 conditional relations/constraints below is what you may do
$ 200\delta_3+ 100\delta_2 \le$ b_chng $\le (200+e)\delta_2 +(100+e)\delta_1 $
$ \sum_{i=1}^3\delta_i = 1$ where $\delta$ are binary and e is a very small number (like $1e-3$).

Then
b_chng_eff= 1st Constr1$\delta_1$+2nd_Constr$\delta_2$+3rd_Constr$\delta_3$

As for the 2nd degree quads for 2 of the above relations, most solvers will be able to accept these constraints. Else you may choose piecewise linearization as suggested here, scroll down to piecewise linear constraints.