"relentlessly increasing" is correct and can be used in written English.
It is typically used to describe something that is continuously and persistently growing or becoming more intense. Example: The cost of living in the city has been relentlessly increasing, making it difficult for many people to afford basic necessities.
Population growth, urbanization and the rapid development of manufacturing industries are relentlessly increasing demand for finite water resources.
The problem is that both models vastly oversimplify the challenge of greatness — for leaders or anyone else — in a world of relentlessly increasing complexity.
The problem is that in the face of relentlessly increasing demand, we're collectively vacationing less and for shorter periods of time.
But that implies that growth in credit is always acceptable as long as the growth rate is steady, even if that growth rate is faster than nominal GDP and even if therefore aggregate leverage is relentlessly increasing.
This is a blow to schools, which are already facing criticism for relentlessly increasing their programme fees despite there being no significant increase in the salaries of the graduates they produce.
It matters that we know exactly how hot our planet can get as we monitor an environment whose temperatures are relentlessly increasing.
But it has relentlessly increased.
For how long can the resources of the earth continue to sustain worldwide growth and relentlessly increased consumption?
For years his party has relentlessly increased its support, yet its northern and southern expressions are growing apart.
From 1965 onwards, as the use of Agent Orange relentlessly increased in Vietnam, he lobbied both his scientific colleagues and the government to stop.
A digital advertising environment on the web – one even more pronounced in mobile – that relentlessly increases the amount of advertising space available and lowers the value of all space overall.
