Selected Publications
since 1988
1. R. Polyak, J. Costa and S. Neyshabouri, Dual Fast Projected Gradient Method for Quadratic Programming [pdf]
2. I. Griva and R. Polyak, Proximal Point Nonlinear Rescaling Method for Convex Optimization [pdf]
3. R. Polyak, Lagrangian Transformation and Interior Ellipsoid Methods in Convex Optimization [pdf]
4. I. Griva and R. Polyak, Primal-Dual Methods for Nonlinear Constrained Optimization [pdf]
5. R. Polyak, Nonlinear Equilibrium vs. Linear Programming [pdf]
6. R. Polyak, On the Local Quadratic Convergence of the Primal-Dual Augmented Lagrangian Method [pdf]
7. R. Polyak,
Primal-Dual Exterior Point Method for Convex Optimization,
Optimization Methods and Software. [pd]
8. R. Polyak, S.-S. Ho and I. Griva,
Support Vector Machine via Nonlinear Rescaling Method,
tentatively accepted by Optimization Letters. [pdf]
9. R. Polyak, Regularized Newton Method for Unconstrained Convex
Optimization, to appear in Math. Program. [pdf]
10. 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]
11. R. Polyak, Nonlinear Rescaling as Interior Quadratic Prox Method in Convex Optimization, to appear in COAP [pdf]
12. I. Griva and R. Polyak, Primal-dual
nonlinear rescaling method with dynamic scaling parameter update, Math. Program., Ser. A 106, 237-259 (2006) [pdf]
13. 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]
14. R. Polyak, Lagrangian Transformation in Convex Optimization, Research Report-072003, Department of SEOR & Mathematical Science Department, GMU, pages 1-23 (2003) [pdf]
15. R. Polyak, Nonlinear rescaling vs. smoothing technique in
convex optimization, Math. Program., Ser. A 92:
197-235 (2002)[pdf]
16. R. Polyak, Log-Sigmoid Multipliers Method in Constrained
Optimization, Annals of Operations Research 101, 427-460 (2001) [pdf]
17. 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]
18. 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]
19. R. Polyak, Modified Interior Distance Functions, Contemporary
Mathematics, AMS, Vol. 209, 183-209 (1997) [pdf]
20. R. Polyak and M. Teboulle,
Nonlinear rescaling and proximal-like methods in convex optimization, Math. Program. 76, 265-284 (1997) [pdf]
21.
A. Melman and R. Polyak, The
Newton modified barrier method for QP problems, Annals of Operations
Research 62, 465-519 (1996) [pdf]
22.
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]
23. 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]
24. 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]
25. R. Polyak, Modified Barrier Functions in Linear Programming,
Research Report IBM T.J. Watson Research Center (1992) [pdf]
26. R. Polyak, Modified Barrier Functions (Theory and Methods),
Math. Program. 54, 177-222 (1992) [pdf]
27. R. Polyak, Smooth Optimization Methods for Minimax Problems, SIAM, J. Control and Optimization, Vol. 26. No. 6 (1988) [pdf]
28. I. Griva and R. Polyak, Numerical results obtained by using Nonlinear Rescaling method on COPS set [pdf]