We should perhaps compute a Jensen's lower bound during an optional "iteration -1". This bound is based on solving a scenario subproblem with the expected value of the uncertain data (which is not always reasonable, but usually is). A solution is produced that could be tested as an upper bound. Here are some thoughts:

• There would need to be a function jensens_creator that is similar to scenario_creator to return the instance for the expected value data (so every "scenario" would have the same data for iteration -1). For most examples, this function is not hard to write, but not completely trivial. Note: when the scenario data is created by sampling a distribution, lazy modelers may choose to fib by using the expected values of the data from the distribution; for small numbers of scenarios, there is a risk of the fib becoming a lie that results in an invalid bound.
• It is easy to construct examples where this bound is much tighter than the so-called trivial bound that we now compute during iteration 0, but it is not always tighter.
• Iteration -1 would not obviate the need for iteration 0 and if iteration 0 were bypassed after iteration -1, iteration 1 would solve the iteration 0 subproblems anyway.