Pyomo多重积分

Question

Is there a continuous (integral) analog to Pyomo's sum function which could do several summations at once

sum(model.x[i,j] for i in model.index_is, for j in model.index_js)

Heat_Conduction.py in the dae examples has a reference to nested integration, but it is commented out and it throws a ValueError: Integral must be indexed by a Continuous S whenever I comment it back in.

# def _obj(m):
#     return Integral(Integral(expr=m.intExp,wrt=m.x,bounds=(0,10)), wrt=m.y,bounds=(0,5))
# m.obj = Objective(rule=_obj)

I've searched everywhere, but I couldn't find a working example and I couldn't understand the docs.

Thanks in advance

Answer 1

The Integral component is not fully developed and I wouldn't recommend using it. A better way to formulate a continuous integral using Pyomo.DAE components would be to differentiate your integral equation and convert it to a differential equation. See the discussion here: How to define an Integral as an objective function in pyomo?