The phrase "dedicated to the problem" is correct and can be used in written English.
You might use it when referring to someone who is dedicated to resolving a particular problem or issue. For example, "John has been dedicated to the problem of air pollution in this city for many years."
This device proved impracticable, but Mergenthaler became dedicated to the problem involved setting type by machine.
"We have a whole team dedicated to the problem of fake reviews," James Kay from TripAdvisor UK told the Guardian.
Some of the men on the Tumblr blog dedicated to the problem (Men Taking Up Too Much Space on Trains) look positively uncomfortable - like they're doing a sitting-down plié or a yoga position.
Postgate's early career was dedicated to the problem of how to use sulphate-reducing bacteria to produce sulphide, which was needed as a source of sulphuric acid for industry.
During the recent decade there were many publications dedicated to the problem of ionospheric storms.
This paper is dedicated to the problem of fault tolerant control for Lipshitz nonlinear system.
This study is dedicated to the problems met with metal-metal bearing prostheses.
The paper is dedicated to the problems of ITER diagnostics caused by effects of radiation from hot DT plasma.
As the granddaughter of Holocaust survivors, I took some satisfaction from the irony a site with a section dedicated to the "Jewish Problem," condemned to wander the wilderness, driven out of one country after another.
In this paper a new local search method is described that is dedicated to the Firefighter Problem (FFP).
To folks like Walker, who have been lighting up online discussion forums dedicated to the Y2K problem, the millennium bug is a prelude to Armageddon.
