The phrase "relentless determination to" is correct and can be used in written English.
It can be used when you need to describe a person, or people, who are determined and refuse to give up in the face of difficulty. For example, "The CEO showed a relentless determination to steer the company to success despite the difficult economic conditions."
He applies the same relentless determination to his hobby, mountain climbing, as he does to writing.
He said: "The keys to school improvement are excellent teaching and leadership and a relentless determination to stamp out failure.
His success came the hard way — he was self-made, with a relentless determination to tell the truth to power and to find truths where others could not.
There is no question that he brought a brash new imagination and relentless determination to City Hall, but those very qualities sometimes alienated, rather than motivated, the people who could help him achieve his goals.
It vividly articulates the mentality that shaped S-21, and indeed Kampuchea beyond, the relentless determination to remove every option from the prisoner – and citizen – to reduce them to absolute compliance.
Her relentless determination to do men's work led to a chain of Buster Keaton-like misadventures -- overturning a farmer's plow, sending her fellow soldiers diving for cover during rifle practice in Spain and ultimately being sent home when, while nearsightedly wandering around the campsite, she stepped into a pot of boiling oil.
The larger issue is the relentless determination of advertisers to see virtually every inch of New York public space as their personal canvas.
Haley Bennett as the determined widow underscores the relentless determination of the crew to overthrow outright tyranny.
Seeing my "support" system, you can imagine the relentless determination, drive and sacrifice it took to earn my bachelors degree -- two, in fact.
His career thundered or faltered more in accordance with the strengths and pitfalls of his relentless ego and determination to be somebody than any believable script.
With his history of prosecutorial investigation of Iran-Contra and BCCI, and now his incredible fortitude in challenging a political machine unrestrained by ethics, he has proved himself a man of relentless courage and determination to see the job through.
