We give an introductory overview of the basics of Robust (convex) Optimization (RO): a methodology aimed at immunizing optimization problems against uncertainty in the data. In Part 1 of the talk, we provide the fundamental definitions and tools, and then introduce RO by discussing robust counterparts of linear programming
(LP) problems affected by deterministic data uncertainty. Besides worst-case immunization, we shall also discuss probabilistic immunization, when data uncertainty is described by a stochastic model.
In Part 2, we extend the RO methodology from LP to second order conic programs (SOCP) and semidefinite programs (SDP) affected by deterministic uncertainty, focusing on tractability and approximation issues. Some applicative examples will illustrate the benefits of the RO approach.