He continued his studies at Rice University, USA, earning a Ph.D. in Applied Mathematics in 1996.

His Ph.D. dissertation, titled Trust-Region Interior-Point Algorithms for a Class of Nonlinear Programming Problems, was supervised by John Dennis.

From 1996 to 2018, Luis Nunes Vicente was a faculty member at the Department of Mathematics[3] of the University of Coimbra, Portugal, becoming full professor in 2009.

He was visiting Chercheur Sénior of the Fondation de Coopération Sciences et Technologies pour l'Aéronautique et l'Espace at CERFACS and IPN Toulouse, during 2010–2015.

[8] With his Ph.D. dissertation, he received the Ralph Budd Thesis Award from Rice University in 1996 and was one of the three finalists of the 94-96 A. W. Tucker Prize of MOS.