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Cubic regularization of Newton method and its global performance

Bibliographic reference Nesterov, Yurii ; Polyak, Boris. Cubic regularization of Newton method and its global performance. In: Mathematical Programming, Série A, Vol. 108, no. 1, p. 177-205 (Août 2006)
Permanent URL http://hdl.handle.net/2078.1/23376
  1. Bennet, A.A.: Newton's method in general analysis. Proc. Nat. Ac. Sci. USA. 2 (10), 592–598 (1916)
  2. Conn, A.B., Gould, N.I.M., Toint, Ph.L.: Trust Region Methods. SIAM, Philadelphia, 2000
  3. Dennis, J.E., Jr., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996
  4. Fletcher, R.: Practical Methods of Optimization, Vol. 1, Unconstrained Minimization. John Wiley, NY, 1980
  5. Goldfeld, S., Quandt, R., Trotter, H.: Maximization by quadratic hill climbing. Econometrica. 34, 541–551 (1966)
  6. Kantorovich, L.V.: Functional analysis and applied mathematics. Uspehi Matem. Nauk. 3 (1), 89–185 (1948), (in Russian). Translated as N.B.S. Report 1509, Washington D.C. (1952)
  7. Levenberg, K.: A method for the solution of certain problems in least squares. Quart. Appl. Math. 2, 164–168 (1944)
  8. Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11, 431–441 (1963)
  9. Nemirovsky, A., Yudin, D.: Informational complexity and efficient methods for solution of convex extremal problems. Wiley, New York, 1983
  10. Nesterov, Yu.: Introductory lectures on convex programming: a basic course. Kluwer, Boston, 2004
  11. Nesterov, Yu., Nemirovskii, A.: Interior-Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia, 1994
  12. Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, NY, 1970
  13. Polyak, B.T.: Gradient methods for minimization of functionals. USSR Comp. Math. Math. Phys. 3 (3), 643–653 (1963)
  14. Polyak, B.T.: Convexity of quadratic transformations and its use in control and optimization. J. Optim. Theory and Appl. 99 (3), 553–583 (1998)