Selected Publications since 1988


1. Complexity of the Regularized Newton Method [pdf]

2. Exterior Distance Function [pdf]

3. Legendre Transformation in Modern Optimization [pdf]

4. Nonlinear Input-Output Equilibrium [pdf]

5. The Projected Gradient Method for Non-negative Least Squares [pdf]

6. R. Polyak, Lagrangian Transformation and Interior Ellipsoid Methods in Convex Optimization [pdf]

7. R. Polyak, J. Costa and S. Neyshabouri, Dual Fast Projected Gradient Method for Quadratic Programming [pdf]

8. I. Griva and R. Polyak, Proximal Point Nonlinear Rescaling Method for Convex Optimization [pdf]

9. R. Polyak, Nonlinear Equilibrium for optimal resource allocation [pdf]

10. I. Griva and R. Polyak, Primal-Dual Methods for Nonlinear Constrained Optimization [pdf]

11.  R. Polyak, Nonlinear Equilibrium vs. Linear Programming [pdf]

12.  R. Polyak, On the Local Quadratic Convergence of the Primal-Dual Augmented Lagrangian Method [pdf]

13.  R. Polyak, Primal-Dual Exterior Point Method for Convex Optimization, Optimization Methods and Software. [pd]

14.  R. Polyak, S.-S. Ho and I. Griva, Support Vector Machine via Nonlinear Rescaling Method, tentatively accepted by Optimization Letters. [pdf]

15.  R. Polyak, Regularized Newton Method for Unconstrained Convex Optimization, to appear in Math. Program. [pdf]

16.  I. Griva and R. Polyak, 1.5-Q-superlinear convergence of an exterior-point method for constrained optimization, to appear in Journal of Global Optimization [pdf]

17.  R. Polyak, Nonlinear Rescaling as Interior Quadratic Prox Method in Convex Optimization, to appear in COAP [pdf]

18.  I. Griva and R. Polyak, Primal-dual nonlinear rescaling method with dynamic scaling parameter update, Math. Program., Ser. A 106, 237-259 (2006) [pdf]

19.  R. Polyak and I. Griva, Primal-Dual Nonlinear Rescaling Method for Convex Optimization, Journal of Optimization Theory and Applications: Vol 122, No 1. 111-156 (2004) [pdf]

20.  R. Polyak, Lagrangian Transformation in Convex Optimization, Research Report-072003, Department of SEOR & Mathematical Science Department, GMU, pages 1-23 (2003) [pdf]

21.  R. Polyak, Nonlinear rescaling vs. smoothing technique in convex optimization, Math. Program., Ser. A 92: 197-235 (2002)[pdf]

22.  R. Polyak, Log-Sigmoid Multipliers Method in Constrained Optimization, Annals of Operations Research 101, 427-460 (2001) [pdf]

23.  R. Polyak, I. Griva and J. Sobieski, Nonlinear Rescaling in Discrete Minimax, in: Nonsmooth/Nonconvex Mechanics: Modeling, Analysis, Numerical Methods, eds. D Gao, R. Ogden and G. Stavroulakis, Kluwer Academic Publisher (2000) [pdf]

24.  D. Goldfarb, R. Polyak, K. Scheinberg and I. Yuzefovich, A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization, Computational Optimization and Applications 14, 55-74 (1999) [pdf]

25.  R. Polyak, Modified Interior Distance Functions, Contemporary Mathematics, AMS, Vol. 209, 183-209 (1997) [pdf]

26.  R. Polyak and M. Teboulle, Nonlinear rescaling and proximal-like methods in convex optimization, Math. Program. 76, 265-284 (1997) [pdf]

27. A. Melman and R. Polyak, The Newton modified barrier method for QP problems, Annals of Operations  Research 62, 465-519 (1996) [pdf]

28. S. Nash, R. Polyak and A. Sofer, A Numerical Comparison of Barrier and Modified-Barrier Methods for Large-Scale Bound-Constrained Optimization, Large Scale Optimization: State of the Art, 319-338 (1994) [pdf]

29. D. Jensen and R. Polyak, The convergence of a modified barrier method for convex programming, IBM J. Res. Develop. 38, No. 3, 307-321 (1994) [pdf]

30. D. Jensen, R. Polyak and Rina Schneur, Numerical Experience with Modified Barrier Functions Method for Linear Programming, Research Report IBM T.J. Watson Research Center (1992) [pdf]

31. R. Polyak, Modified Barrier Functions in Linear Programming, Research Report IBM T.J. Watson Research Center (1992) [pdf]

32. R. Polyak, Modified Barrier Functions (Theory and Methods), Math. Program. 54, 177-222 (1992) [pdf]

33. R. Polyak, Smooth Optimization Methods for Minimax Problems, SIAM, J. Control and Optimization, Vol. 26. No. 6 (1988) [pdf]

34. I. Griva and R. Polyak, Numerical results obtained by using Nonlinear Rescaling method on COPS set [pdf]