can machine learning/Deep learning used to minimize an objective function?
We actually wrote this for an engineering company. Basically we modeled the project business processes, then decomposed them to metrics for analysis. I can high level three cost savings areas we found.

Purchasing: use receipts, billing, and time metrics to identify outliers and reconciliation failures (receipts != payments). Outliers/missing may indicate mistakes or fraud/theft/overcharging in billing (ie:$200 hammer). Used filter functions to find.

Contract and Permit analysis: make sure all required permits and contract provisions are in place. Used text classification and boolean (exception reporting, really).

Project length prediction: if a project is shorter or longer than others in it's class, investigate. Used statistical analysis (the client already classified: public/private, plumbing/sewage, location, etc).

This was before TensorFlow, which likely could improve on our results. You will find that there are plenty of features (metrics) to model in these processes.

So hopefully this can help on model definition and  consequently the objective functions.