"to overcome the problem" is correct and usable in written English.
For example, you could use it in a sentence like: "We need to come up with a creative solution to overcome the problem."
"We are going to overcome the problem".
To overcome the problem, Dr. Neal-Barnett makes a strong case for support groups.
Indian finance provider InVenture has developed a mobile application that promises to overcome the problem.
This would give Britain time to train more doctors and so help to overcome the problem.
"The challenge is to develop more rapid diagnosis to overcome the problem of tracking the pandemic.
One way to overcome the problem is to trick the meter.
The Canon EF 28-to-135-millimeter I.S. zoom lens ($480; canonusa.com) uses electronics to overcome the problem.
As a result, we take these issues very seriously and have been working hard to overcome the problem.
First, in order to overcome the problem of capacity shortages, Britain needs to move to double-decker trains.
MRT aims to overcome the problem by replacing the mother's defective mitochondria with those from a healthy donor.
There are currently few alternatives to overcome the problem.
