The phrase "assert a commitment to" is correct and usable in written English.
You can use it when expressing a strong declaration of dedication or promise towards a particular cause, goal, or principle.
Example: "The organization aims to assert a commitment to sustainability in all its operations."
Alternatives: "declare a commitment to" or "affirm a dedication to".
The Plaza responded to the lawsuit yesterday with a statement asserting a commitment to diversity, and called some of the allegations unfounded.
Heath 30 asserts that a commitment to uncertainty is fundamental to general practice… and Schon 31 has described this operative landscape as a 'swampy lowland' proposing a model which advocates reflective practice as the key to dealing with uncertainty.
5)—according to which (à la Brandom 1983), in asserting p one undertakes a commitment to either defending p or giving up p if the challenge cannot be met satisfactorily (see Kölbel (2004: 308) for some other discussions of this objection).
The agreement contains several enumerated points asserting a general commitment to the idea that "climate change is one of the greatest challenges of our time" and asserts that "deep cuts" in global emissions were required.
Just this week, the newly combined Yoox Net-A-Porter climbed on its first listing on the Milan stock exchange, and LVMH (owner of Louis Vuitton and Moët & Chandon) has asserted a serious commitment to e-commerce.
Nonaligned states assert their right to pursue independent policies away from a commitment to any of the existing alliances headed by the superpowers.
Or will we act and assert the real American values of hard work and responsibility, a commitment to a vibrant middle class, to college affordability, and the opportunity to reach the American Dream?
The interviewed planners thus assert that they have direct contact with many citizens who express a commitment to strong standards of traffic safety for particularly vulnerable travelers such as children, bicyclists and pedestrians.
If this is right, then incurring a commitment to truth is not sufficient for asserting.
Champions of stimulus assert that another huge round of public spending or monetary easing — maybe even a commitment to higher inflation and government borrowing — will jump-start the engine.
