"complicated challenge" is correct and usable in written English.
You can use it when you are referring to a task or problem that is difficult to complete or solve. For example, "I had to face a complicated challenge when I tried to build the new computer."
They were both a really complicated challenge".
That was no easy feat in a negotiation over an immensely complicated challenge involving nearly 200 countries, and half a dozen rival negotiating blocs.
But though it may not seem much to ask, it is a horrendously complicated challenge to get from the NHS and care services we have today, to that simpler-seeming and more patient-focused vision.
It's a highly complicated challenge involving a very delicate political dance around minefields.
Reading the genome, now that we have it, is a fantastically complicated challenge.
Beyond the already complicated challenge of traditional interviews, assessments scales and psychometric batteries attempting to capture different degrees of emotions, feelings, thoughts, and behaviours, these instruments also have to deal with the inter-rater, cultural and linguistic differences mining their uniform standardization (Nordgaard et al. 2013).
Still, none of them have anything like the sophisticated management strategies used by American business, medicine or the military for addressing complicated challenges.
There is more than one Democratic National Convention taking place here, reflecting what has emerged as one of Mr. Kerry's most complicated challenges this week: making the case for Mr. Kerry to independent voters while feeding the beast that is the hard-core Democrats, the heart and soul of this party.
Members of underrepresented groups, such as Professor Jones, face complicated challenges when deciding who and how to mentor.
Especially in the natural sciences, E-learning faces more complicated challenges than disciplines like social sciences: physical presence in a lab with on hands-experience can hardly be replaced by online courses with videoconferences from a remote laboratory.
There is something very basic about the construction, but at the same time, within each one there's some really complicated challenges, I have to say.
