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Volumn 162, Issue 1-2, 2017, Pages 1-32

A trust region algorithm with a worst-case iteration complexity of O(ϵ- 3 / 2) for nonconvex optimization

Author keywords

Global convergence; Local convergence; Nonconvex optimization; Nonlinear optimization; Trust region methods; Unconstrained optimization; Worst case evaluation complexity; Worst case iteration complexity

Indexed keywords

FUNCTION EVALUATION; NONLINEAR PROGRAMMING;

EID: 84969228222     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-016-1026-2     Document Type: Article
Times cited : (182)

References (16)
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    • Toint, Ph.L.: On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. SIAM
    • Cartis, C., Gould, N.I.M., Toint, Ph.L.: On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. SIAM J. Optim. 20(6), 2833–2852 (2010)
    • (2010) J. Optim , vol.20 , Issue.6 , pp. 2833-2852
    • Cartis, C.1    Gould, N.I.M.2
  • 4
    • 79952763936 scopus 로고    scopus 로고
    • Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results
    • Cartis, C., Gould, N.I.M., Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results. Math. Program. 127, 245–295 (2011)
    • (2011) Math. Program , vol.127 , pp. 245-295
    • Cartis, C.1    Gould, N.I.M.2
  • 5
    • 81255179401 scopus 로고    scopus 로고
    • Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity
    • Cartis, C., Gould, N.I.M., Toint, Ph.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function- and derivative-evaluation complexity. Math. Program. 130, 295–319 (2011)
    • (2011) Math. Program , vol.130 , pp. 295-319
    • Cartis, C.1    Gould, N.I.M.2
  • 6
    • 82555186046 scopus 로고    scopus 로고
    • Toint. Ph.L.: Optimal Newton-type methods for nonconvex smooth optimization problems
    • School of Mathematics, University of Edinburgh
    • Cartis, C., Gould, N.I.M., Toint. Ph.L.: Optimal Newton-type methods for nonconvex smooth optimization problems. Technical report ERGO 11-009, School of Mathematics, University of Edinburgh (2011)
    • (2011) Technical report ERGO , vol.11-9
    • Cartis, C.1    Gould, N.I.M.2
  • 7
    • 85056067384 scopus 로고    scopus 로고
    • Toint, Ph.L.: Trust-Region Methods. Society for Industrial and Applied Mathematics (SIAM)
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000)
    • (2000) Philadelphia
    • Conn, A.R.1    Gould, N.I.M.2
  • 9
    • 79952771183 scopus 로고
    • The modification of Newton’s method for unconstrained optimization by bounding cubic terms. Technical report NA/12, Department of Applied Mathematics and Theoretical Physics
    • Griewank, A.: The modification of Newton’s method for unconstrained optimization by bounding cubic terms. Technical report NA/12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge (1981)
    • (1981) University of Cambridge
    • Griewank, A.1
  • 12
    • 33646730150 scopus 로고    scopus 로고
    • Cubic regularization of Newton’s method and its global performance
    • Nesterov, Yu., Polyak, B.T.: Cubic regularization of Newton’s method and its global performance. Math. Program. 108(1), 117–205 (2006)
    • (2006) Math. Program. , vol.108 , Issue.1 , pp. 117-205
    • Nesterov, Y.1    Polyak, B.T.2
  • 16
    • 33947606578 scopus 로고    scopus 로고
    • Affine conjugate adaptive Newton methods for nonlinear elastomechanics
    • Weiser, M., Deuflhard, P., Erdmann, B.: Affine conjugate adaptive Newton methods for nonlinear elastomechanics. Optim. Methods Softw. 22(3), 413–431 (2007)
    • (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.