메뉴 건너뛰기




Volumn 27, Issue 2, 2012, Pages 197-219

Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization

Author keywords

cubic regularization; Newton's method; nonlinear optimization

Indexed keywords

COMPLEXITY RESULTS; CONVEX OBJECTIVES; CONVEX PROBLEMS; CUBIC REGULARIZATION; GLOBAL PERFORMANCE; GLOBAL SOLUTIONS; NEWTON'S METHODS; NONCONVEX; NONLINEAR OPTIMIZATION; NUMERICAL RESULTS; REGULARISATION; REGULARIZATION ALGORITHMS; REGULARIZATION METHODS; SECOND ORDERS; UNCONSTRAINED OPTIMIZATION; UPPER BOUND; WORST-CASE EFFICIENCY;

EID: 84859180670     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2011.602076     Document Type: Article
Times cited : (26)

References (13)
  • 2
    • 82555186040 scopus 로고    scopus 로고
    • On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
    • University of Edinburgh, Edinburgh
    • C. Cartis, N.I.M. Gould, and Ph.L. Toint, On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization, ERGO Tech. Rep. 10-005, School of Mathematics, University of Edinburgh, Edinburgh, 2010.
    • (2010) ERGO Tech. Rep. 10-005, School of Mathematics
    • Cartis, C.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 3
    • 79251493375 scopus 로고    scopus 로고
    • On the complexity of steepest descent, newton's and regularized newton's methods for nonconvex unconstrained optimization
    • C. Cartis, N.I.M. Gould, and Ph.L. Toint, On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization, SIAM J. Optim. 20(6) (2010), pp. 2833-2852.
    • (2010) SIAM J. Optim. , vol.20 , Issue.6 , pp. 2833-2852
    • Cartis, C.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 4
    • 81255179401 scopus 로고    scopus 로고
    • Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity
    • doi:10.1007/s10107-009-0337-y (online)
    • C. Cartis, N.I.M. Gould, and Ph.L. Toint, Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity, Math. Program. (2010), doi:10.1007/s10107-009- 0337-y (online).
    • (2010) Math. Program
    • Cartis, C.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 5
    • 79952763936 scopus 로고    scopus 로고
    • Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results
    • C. Cartis, N.I.M. Gould, and Ph.L. Toint, Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results, Math. Program. 127(2) (2011), pp. 245-295.
    • (2011) Math. Program , vol.127 , Issue.2 , pp. 245-295
    • Cartis, C.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 8
    • 0005658675 scopus 로고    scopus 로고
    • Reprinted as SIAM, Philadelphia, PA
    • Reprinted as Classics in Applied Mathematics 16, SIAM, Philadelphia, PA, 1996.
    • (1996) Classics in Applied Mathematics , vol.16
  • 11
    • 34547474583 scopus 로고    scopus 로고
    • Accelerating the cubic regularization of newton's method on convex problems
    • Yu. Nesterov, Accelerating the cubic regularization of Newton's method on convex problems, Math. Program. 112(1) (2008), pp. 159-181.
    • (2008) Math. Program , vol.112 , Issue.1 , pp. 159-181
    • Nesterov, Yu.1
  • 12
    • 33646730150 scopus 로고    scopus 로고
    • Cubic regularization of newton's method and its global performance
    • Yu. Nesterov and B.T. Polyak, Cubic regularization of Newton's method and its global performance, Math. Program. 108(1) (2006), pp. 177-205.
    • (2006) Math. Program , vol.108 , Issue.1 , pp. 177-205
    • Nesterov, Yu.1    Polyak, B.T.2
  • 13
    • 33947606578 scopus 로고    scopus 로고
    • Affine conjugate adaptive newton methods for nonlinear elastomechanics
    • M. Weiser, P. Deuflhard, and B. Erdmann, Affine conjugate adaptive Newton methods for nonlinear elastomechanics, Optim. Methods Softw. 22(3) (2007), pp. 413-431.
    • (2007) Optim. Methods Softw. , vol.22 , Issue.3 , pp. 413-431
    • Weiser, M.1    Deuflhard, P.2    Erdmann, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.