We have been involved in solving problems in many areas, including trajectory optimization, portfolio optimization, power system optimization, and structural optimization. Robustness starts but does not end with being able to prove an algorithm converges. There is a choice is how to implement an algorithm and all differ very slghtly from the theoretical algorithm. Despite the differences being small they sometimes have a catastrophic affect on an algorithm's performance. The trick is to choose an implementation that closely preserves an algorithm's the theoretical properties.
Efficiency is a never-ending battle.
No matter how efficient an algorithm, there is always a need for it to run faster. New applications that are harder or larger result from the current success.