Is there any literature on constrained nonlinear optimization where constraint returns have to be queried from an oracle?

Question

I am looking at literature considering constrained optimization problems of the form:

$\min_{x\in X\subseteq R^n} f(x), \text{ subject to } g_{oracle}(x) \leq 0$

The optimization algorithm doesn't know $g_{oracle}(\, .\,)$ in closed form, but rather has to query the value of $g_{oracle}(x)$ from an oracle for a given value of $x$. Further, $g_{oracle}$ may or may be able to return gradients with respect to $x$.

This is motivated by the Optimal Power Flow problem in electricity grids, which aims to optimize electricity costs subject to the physics of transferring electricity across the grid. Currently, OPF is solved by representing physics as linear or convex constraints, which are often low-fidelity. On the other hand, there do exist high-fidelity power flow simulators which do a better job of representing the physics. They correspond to the $g_{oracle}$ in the above formulation.

There are some papers in the power systems domain which use the above formulation in a Reinforcement Learning framework. However, I'm curious if there exists literature which considers general optimization problems of the above form?

Answer 1

If $g_{oracle}(x)$ can return gradients, then this is a standard nonlinear optimization problem which can be passed directly to an oracle-based solver like Ipopt (https://github.com/coin-or/Ipopt). Ipopt does not need to know the nonlinear expressions in closed form.

In fact, if you write an optimal power flow formulation in an algebraic modeling language like AMPL, JuMP, or Pyomo, the first thing they do is convert the algebraic representation into an oracle that can be queried by the solver (as well as compute oracles for the relevant derivatives).

If $g_{oracle}(x)$ cannot return gradients, then you would need to use a derivative-free solver. There are a variety of solvers, including algorithms implemented in https://nlopt.readthedocs.io/en/latest/ or https://github.com/coin-or/rbfopt.