- Conic quadratic problems are convex construction.
- They are almost as simple as LPs to deal with in software.
- Duality theory is almost as simple as the linear case.
- The (Nesterov-Todd) primal-dual algorithm for conic quadratic problems is extremely good.
I had feared that the distinguished audience would consider my talk too simple. However, the speaker before me was Bob Fourer of AMPL. The title of his talk was about checking convexity of general optimization problems formulated in AMPL and it had two parts. The first part was about checking convexity and the second part was about how you in some cases automatically could convert optimization problems on functional form to a conic quadratic optimization problem. So the two talks complemented each other very well and it made me feel better about my talk.
Finally, I would like to mention that Yurii Nesterov was one of the speakers. He must have enjoyed the day since two speakers was talking about his baby named optimization over symmetric cones.