I’m surprised we aren’t asking what performance problems you are having!
In my experience, performance problems are usually tied to specific conditions and situations. Design patterns, on the other hand, are solutions to more general and abstract problems. It would seem a bit awkward to approach both in the same text: what of possibly many "non-patterned" solutions should the author compare the performance of a design pattern against? When the performance problem is general, there certainly already are patterns to solve them: the Flyweight is a good example.
The penalties imposed by the use of a design pattern are of a finite, very small set: introduction of virtual calls, added latency due to delegation, extra memory consumption due to the proliferation of objects and so on. If, after profiling, you notice that these are the cause of your woes, there are known ways to minimize them.
Knowing the patterns might be useful to solve performance issues, too. First, someone already mentioned that patterns break down a problem in smaller bits: this might ease pinpointing the source of the issue and isolating ugly but performant code. They also create a framework of reasoning and expectations for developers. If you must introduce a deviation for performance reasons, it will be obvious: “Except here, where we forego X and do Y to improve performance, this is a Chain of Responsibility.” They are rules to be broken when needed.
(Alas, there is one very good pattern for getting good performance: measure, pinpoint, fix.)