Accelerating the cubic regularization of Newton's method on convex problems

Mathematical Programming

Volumn 112, Issue 1, 2008, Pages 159-181

  Nesterov, Yu ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Condition number; Convex optimization; Cubic regularization; Global complexity bounds; Newton's method; Non degenerate problems; Unconstrained minimization; Worst case complexity

Indexed keywords

BRANCH AND BOUND METHOD; COMPUTATIONAL COMPLEXITY; CONSTRAINED OPTIMIZATION; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PROBLEM SOLVING;

CONDITION NUMBERS; CONVEX OPTIMIZATION; CONVEX PROBLEMS; CUBIC REGULARIZATION; GLOBAL COMPLEXITY BOUNDS; NON-DEGENERATE PROBLEMS; UNCONSTRAINED MINIMIZATION; WORST-CASE COMPLEXITY;

QUADRATIC PROGRAMMING;

EID: 34547474583     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0089-x     Document Type: Conference Paper

References (9)

1. Bennet A.A. (1916). Newton's method in general analysis. Proc. Nat. Ac. Sci. USA. 2(10): 592-598
2. Conn A.B., Gould N.I.M. and Toint Ph.L. (2000). Trust Region Methods. SIAM, Philadelphia
3. Dennis J.E.Jr. and Schnabel R.B. (1996). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia
4. Kantorovich, L.V.: Functional analysis and applied mathematics. Uspehi Matem. Nauk. 3(1), 89-185 (1948), (in Russian).
5. Translated as N.B.S. Report 1509, Washington (1952)
6. Nesterov Yu. (2004). Introductory Lectures on Convex Programming. A Basic Course. Kluwer, Boston
7. Nesterov Yu. and Polyak B. (2006). Cubic regularization of Newton method and its global performance. Math. Program. 108(1): 177-205
8. Ortega J.M. and Rheinboldt W.C. (1970). Iterative Solution of Nonlinear Equations in Several Variables. Academic, NY
9. Vladimirov, A., Nesterov, Yu., Chekanov, Yu.: Uniformly convex functionals. Vestnik Moskovskogo universiteta, ser. Vychislit. Matem. i Kibern., 4, 18-27 (1978), (In Russian)