Dr. Monteiro’s research is confined largely to the continuous optimization area with specific interest in interior-point algorithms for linear programming, semidefinite programming, convex programming and complementarity problems. He is also interested in computational optimization with specific interest in the development of numerical codes for solving large scale semidefinite programs. His most recent works deal with the development of heuristics for graph problems (e.g., maximum cut or maximum clique problems) that finds nearly optimal solutions by reformulating the discrete problem into a continuous one and then solving it by some standard nonlinear programming algorithm. Dr. Monteiro’s research has been supported by the National Science Foundation and the Office of Naval Research. He remains actively involved in research and academic activities associated with the Ph.D. program in Algorithms, Combinatorics, and Optimization (ACO) which is a multidisciplinary effort sponsored by ISyE, the School of Mathematics, and the College of Computing.
Due to his widely cited research work, Dr. Monteiro joined in 2004 the list of ISI Highly Cited Researchers in the Mathematics category.