Roman Polyak Professor Office: Science & Technology Building II, Room 127 Phone: (703) 993-1685 Fax: (703) 993-1521 E-mail: rpolyak@gmu.edu Personal Homepage: mason.gmu.edu/~rpolyak/

Education

• Ph.D., 1966, Moscow Central Institute of Mathematics and Economics at the U.S.S.R. Academy of Sciences

• M.S. (honors), 1963, Kiev State University, mathematics and physics
  

Research

• Linear and Nonlinear Programming

• Game Theory

• Mathematical Economics
  

Recent Papers

• Lagrangian Transformation in convex optimization, Research Report 072004, Department of SEOR and Mathematical Sciences Department, GMU 2004 (submitted to Mathematical Programming)

• Primal-Dual Nonlinear Rescaling method with dynamic scaling parameter update? to appear in Mathematical Programming, 2004, with I.Griva

• Primal-Dual Nonlinear Rescaling Methods for Convex Optimization, Journal Optimization Theory &Applications (JOTA) v122, n1, 2004 p111-156, with I. Griva

• Optimal Transformer Tap Selection Using Modified Barrier ?Augmented Lagrangian method, IEEE Transaction on Power Systems vol 18 n 1 p251-257, 2002, with M. Adibi, I.Griva, L.Mili

• Nonlinear Rescaling vs. Smoothing Technique in Constrained Optimization, Mathematical Programming, 92:197-235, 2002

• Log-Sigmoid Multipliers Method in Constrained Optimization, Annals of Operations Research 101, 427-460, 2001

• Barrier Functions and their Modifications, Encyclopedia of Operations Research, Kluwer Academic Press, 2000

• Nonlinear Rescaling in Discrete Minimax in: Nonsmooth / Nonconvex Mechanics: Modeling, Analysis, Numerical Methods, eds. D. Gao, R. Ogden, G. Stavroulakis, Kluwer Academic Publisher, 2000, with I. Griva, J. Sobieski

• Modified Barrier-Augmented Lagrangian Method for Constrained Minimization, Computational Optimization and Applications, 14, p 55-74, 1999, with D. Goldfarb, K. Mints, I. Yuzefovich

• The Newton Log-Sigmoid method in Constrained Optimization, Proceedings of the AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998 St. Louis, with I. Griva and J. Sobieski

• Modified Interior Distance Functions in Optimization Methods in Partial Differential Equations. Series: Contemporary Mathematics Vol 209, AMS 1997

• Nonlinear Rescaling and Proximal-like Methods in Convex Programming, Mathematical Programming 76 (1997) 265-284, with M. Teboulle

• The Newton Modified Barrier Method for QP Problems, Annals of Operations Research, 62, pp. 465-519, 1996, with A. Melman

• Barrier and Distance Functions in Constrained Optimization, Encyclopedia of Operations Research, Kluwer, Academic Press, 1995

• Structural Optimization Using Newton Modified Barrier Method, Structural Optimization, v. 10, n. 3, 1995, with L. Berke, N. Khot, R. Schneur

• A Numerical Comparison of Barrier and Modified-Barrier Methods for Large-Scale Bound-Constrained Optimization, 1994, Large-Scale Optimization: State of the Art, Kluwer Academic, with S. Nash and A. Sofer

• The Convergence of MBF Method for Convex Programming, IBM Journal of Research and Developments, Vol. 38 pp. 307-321, 1994, with D. Jensen

• Modified Barrier Functions in Linear Programming, IBM Research Report, RC 17790 (No. 78331), pp. 1-55, 1992

• Modified Barrier Functions (Theory and Methods), Mathematical Programming, 54, No. 2, pp. 177-222, 1992

• Smooth Optimization Methods for Minimax Problems, SIAM J Control and Optimization, Vol. 26, No. 6, 1988

Awards

• Fulbright Scholarship Award in 2001

• NSF and NASA Awards 1993, 1994, 1997, 2003

• IFREE (International Foundation for Research in Experimental Economics) Fellow 2003