In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set and the decision-maker protects the system against the worst case within that set.
In the context of nonlinear multi-stage max-min robust optimization problems:
What are the best robustness models such as Strict robustness, Cardinality constrained robustness, Adjustable robustness, Light robustness, Regret robustness, and Recoverable robustness?
How to solve max-min robust optimization problems without linearization/approximations efficiently? Algorithms?
How to approach nested robust optimization problems?
For example, the problem can be security-constrained AC optimal power flow.
We provide a concise introduction to modern methods for solving nonlinear optimization problems.
We consider both linesearch and trust-region methods for unconstrained minimization, interiorpoint
methods for problems involving inequality constraints, and SQP methods for those involving
equality constraints. Theoretical as well as practical aspects are emphasised. We conclude by giving
a personal view of some of the most signi cant papers in the area, and a brief guide to on-line
resources.
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