After emigration from the former Soviet Union in 1988, he was a visiting scientist at the Mathematical Sciences Department at the T.J. Watson Research Center IBM. He was a principal investigator of a joint IBM and NASA study "Optimization in Structural Design." 

 He developed the Nonlinear Rescaling (NR) theory and methods for constrained optimization -an   alternative to SUMT .The NR theory allows eliminating the basics drawbacks of the classical barrier and distance functions and correspondent SUMT methods for Nonlinear Programming (NLP). In particular, his Modified Barrier Functions methods had been used with great success for solving large scale real life NLP problems including planning radiation therapy ,truss topology design, optimal power flow, antenna design  just to mention a few.
During the last few years together with his former PhD student Dr.I.Griva he developed Primal-Dual NR theory and methods that can be considered as an alternative to the Interior Point Methods for NLP.

   He is the author and co-author of six monographs and chapters of books and he has published more than fifty papers in refereed professional journals. His area of expertise is Linear and Nonlinear programming (interior-exterior point methods), game theory and mathematical economics.

 Dr. R. Polyak joined the faculty of George Mason University in January 1993. Since 1995 he is a full professor of mathematics and operations research. He has a joint appointment at the Mathematical Sciences and Systems Engineering & Operations Research departments.  During the last 15 years he received several NSF and NASA Awards for his work in NLP.

 He received the Fulbright Scholarship Award in 2001 for his work on NR theory and applications of the NR methods for solving real life problems.   In 2003 he became an IFREE (International Foundation for Research in Experimental Economics) Fellow for his work in Mathematical Economics.