The phrase "ambitious task for" is correct and usable in written English.
It can be used when describing a challenging or demanding assignment or project that is intended for someone or a group to undertake.
Example: "Completing the marathon was an ambitious task for the entire team, but they were determined to succeed."
Alternatives: "challenging endeavor for" or "daunting project for".
Finding witnesses presented an ambitious task for Ms. Kempner.
It is an ambitious task for a non-programmer, but thanks to Appinventor technology participants were able to build a working competition robot's software in just two days!
Developing a new analytical methodology to define, thanks to the compressor polynomial expression, the condensing unit performances like: cooling capacity, condensing temperature and the power consumption with only evaporating temperature and ambient, is an ambitious task for engineer.
Taking on the issue of cabdriver attire may be an ambitious task for a city agency that still struggles to meaningfully impose basic, arguably more pressing rules of the road: keep to the speed limit; hang up that cellphone.
In presenting "India: Public Places, Private Spaces — Contemporary Photography and Video Art," the Newark Museum set an ambitious task for itself: to dazzle visitors while reaching out to New Jersey's growing South Asian community.
In this respect, the goal of achieving an optimum design for an adsorption process is an ambitious task for which a thoughtful knowledge of batch kinetics is necessary.
The École Polytechnique was established in 1794 with the ambitious task of preparing all candidates for the specialist civil and military engineering schools of the republic.
Gary Street's side have set themselves the ambitious task of going unbeaten in this competition, before challenging for the title of world champions.
Realizing the inadequacy of current criteria for assigning species to their appropriate genera, he undertook the ambitious task of compiling an unambiguous descriptive classification of all seed plants.
Patrick K. Jjemba, a senior research analyst for innovation and technology with American Water, takes on the ambitious task of framing the complex issue of PPCPs in the environment.
He next undertook the most ambitious task of preparing a descriptive classification of all known seed plants, Prodromus Systematis Naturalis Regni Vegetabilis (17 vol., 1824 73), for which he prepared the first seven volumes.
