Which preposition is correct to use in the following sentence?:
Implementation of this technique for/in/on/with complex objects is complicated
(meaning: it is complicated to apply this technique to complex objects.)
There's no single correct usage here.
If you use in, that means you're implementing the technique inside of a complex object (for instance, it could be a piece of code contained within the object, or a piece of machinery inside of it). If you use for, then you're saying the technique operates on complex objects or for the benefit of complex objects. If you use with, you're implying that the technique is in conjunction with complex objects. On, however, does not "feel" right in conjunction with "implementation."
Given the meaning you're seeking, for seems like the best alternative.