in the face of

クリミア住民投票を受け、ロシアのプーチン大統領はクリミアは「分かつことのできない」ロシアの一部だと述べ、編入条約に署名をしました。

Putin Calls Crimea an ‘Integral’ Part of Russia

Moving swiftly in the face of international condemnation, President Vladimir V. Putin declared his intention to make Crimea a part of the Russian Federation, defying the United States and Europe just hours after they imposed their first financial sanctions against Moscow since the crisis in Ukraine began.

“Crimea has always been an integral part of Russia in the hearts and minds of people,” Mr. Putin declared in remarks that reached deep into Russian and Soviet history to justify the move. “That faith has been preserved and passed on from generation to generation.”

Mr. Putin spoke in St. George’s Hall in the Grand Kremlin Palace before Russia’s entire political elite, including members of both houses of Parliament and the governors of the country’s regions. He spoke hours after he submitted the legislation to begin the process of annexation after a vote to secede from Ukraine that was hastily organized and conducted under the watch of thousands of Russian special operations troops.

http://www.nytimes.com/2014/03/19/world/europe/ukraine.html?emc=edit_na_20140318

in the face ofは字面では「〜の顔前で」ということですが、「〜を物ともせずに」という比喩的な意味で用いられます（cf. in the teeth of）。

ただおなじみのdespiteやin spite ofと違うのは、英英辞典にも１）despite something 、２）when threatened by somethingという定義があるように（Cambridge Dictionary of American Idioms）、「脅しや圧力などにもかかわらず〜する」という含意のあるイディオムです。
ネットの辞書には、If people act in the face of something, they do it despite it or when threatened by it.という定義がありました。（UG）

cf. http://www.usingenglish.com/reference/idioms/in+the+face+of.html#uEgettoAVLIvkjaH.99