메뉴 건너뛰기




Volumn 32, Issue 4, 2012, Pages 1662-1695

An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity

Author keywords

convex constraints; cubic regularization regularization; global convergence; nonlinear optimization; numerical algorithms; worst case complexity

Indexed keywords

NONLINEAR PROGRAMMING;

EID: 84867521936     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drr035     Document Type: Article
Times cited : (85)

References (20)
  • 1
    • 79952763936 scopus 로고    scopus 로고
    • Adaptive cubic regularisation methods for unconstrained optimization. Part i: Motivation, convergence and numerical results
    • CARTIS, C., GOULD, N. I. M. & TOINT, PH. L. (2011a) Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295.
    • (2011) Math. Program. , vol.127 , pp. 245-295
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.H.L.3
  • 3
    • 81255179401 scopus 로고    scopus 로고
    • 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. (2011b) Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity. Math. Program., 130, 295-319.
    • (2011) Math. Program. , vol.130 , pp. 295-319
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.H.L.3
  • 4
    • 79251493375 scopus 로고    scopus 로고
    • On the complexity of steepest descent, newton's and regularized newton's methods for nonconvex unconstrained optimization
    • CARTIS, C., GOULD, N. I. M. & TOINT, PH. L. (2010) On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization. SIAM J. Optimization, 20, 2833-2852.
    • (2010) SIAM J. Optimization , vol.20 , pp. 2833-2852
    • Cartis, C.1    Gould, N.I.M.2    Toint, P.H.L.3
  • 5
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization with simple bounds
    • See also same journal 26 764-767
    • CONN, A. R., GOULD, N. I. M. & TOINT, PH. L. (1988) Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM J. Numer. Anal., 25, 433-460. See also same journal 26, 764-767.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint Ph., L.3
  • 6
    • 0003951723 scopus 로고    scopus 로고
    • Number 01 in 'MPS- SIAM Series on Optimization'. Philadelphia, PA: SIAM
    • CONN, A. R., GOULD, N. I. M. & TOINT, PH. L. (2000) Trust-Region Methods. Number 01 in 'MPS-SIAM Series on Optimization'. Philadelphia, PA: SIAM.
    • (2000) Trust-Region Methods
    • Conn, A.R.1    Gould, N.I.M.2    Toint Ph., L.3
  • 7
    • 0002709547 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints
    • CONN, A. R., GOULD, N. I. M., SARTENAER, A. & TOINT, PH. L. (1993) Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints. SIAM J. Optimization, 3, 164-221.
    • (1993) SIAM J. Optimization , vol.3 , pp. 164-221
    • Conn, A.R.1    Gould, N.I.M.2    Sartenaer, A.3    Toint, P.H.L.4
  • 8
    • 55849087653 scopus 로고    scopus 로고
    • A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization
    • GRATTON, S., MOUFFE, M., TOINT, PH. L. & WEBER-MENDONÇ A, M. (2008a) A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization. IMA J. Numer. Anal., 28, 827-861.
    • (2008) IMA J. Numer. Anal. , vol.28 , pp. 827-861
    • Gratton, S.1    Mouffe, M.2    Toint Ph., L.3    Weber-Mendonç, A.M.4
  • 9
    • 61349175317 scopus 로고    scopus 로고
    • Recursive trust-region methods for multiscale nonlinear optimization
    • GRATTON, S., SARTENAER, A. & TOINT, PH. L. (2008b) Recursive trust-region methods for multiscale nonlinear optimization. SIAM J. Optimization, 19, 414-444.
    • (2008) SIAM J. Optimization , vol.19 , pp. 414-444
    • Gratton, S.1    Sartenaer, A.2    Toint, P.H.L.3
  • 12
    • 0013240063 scopus 로고
    • Inequalities for stochastic nonlinear programming problems
    • MANGASARIAN, O. L. & ROSEN, J. B. (1964) Inequalities for stochastic nonlinear programming problems. Oper. Res., 12, 143-154.
    • (1964) Oper. Res. , vol.12 , pp. 143-154
    • Mangasarian, O.L.1    Rosen, J.B.2
  • 13
    • 0003696537 scopus 로고    scopus 로고
    • Applied Optimization. Dordrecht, The Netherlands: Kluwer Academic Publishers
    • NESTEROV, YU. (2004) Introductory Lectures on Convex Optimization. Applied Optimization. Dordrecht, The Netherlands: Kluwer Academic Publishers.
    • (2004) Introductory Lectures on Convex Optimization
    • Nesterov, Y.1
  • 15
    • 33646730150 scopus 로고    scopus 로고
    • Cubic regularization of newton method and its global performance
    • NESTEROV, YU. & POLYAK, B. T. (2006) Cubic regularization of Newton method and its global performance. Math. Program., 108, 177-205.
    • (2006) Math. Program. , vol.108 , pp. 177-205
    • Nesterov, Y.U.1    Polyak, B.T.2
  • 16
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • ROCKAFELLAR, R. T. (1970) Convex Analysis. Princeton, NJ: Princeton University Press.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 17
    • 26444518362 scopus 로고
    • Armijo-type condition for the determination of a generalized cauchy point in trust region algorithms using exact or inexact projections on convex constraints
    • SARTENAER, A. (1993) Armijo-type condition for the determination of a generalized Cauchy point in trust region algorithms using exact or inexact projections on convex constraints. Belg. J. Oper. Res. Stat. Comput. Sci., 33, 61-75.
    • (1993) Belg. J. Oper. Res. Stat. Comput. Sci. , vol.33 , pp. 61-75
    • Sartenaer, A.1
  • 18
    • 0003523947 scopus 로고
    • International Series of Monographs on Computer Science, Oxford: Oxford University Press
    • VAVASIS, S. A. (1991) Nonlinear Optimization: Complexity Issues, International Series of Monographs on Computer Science, vol. 8. Oxford: Oxford University Press.
    • (1991) Nonlinear Optimization: Complexity Issues , vol.8
    • Vavasis, S.A.1
  • 19
    • 0010932634 scopus 로고
    • Black-box complexity of local minimization
    • VAVASIS, S. A. (1993) Black-box complexity of local minimization. SIAM J. Optimization, 3, 60-80.
    • (1993) SIAM J. Optimization , vol.3 , pp. 60-80
    • Vavasis, S.A.1
  • 20
    • 33947606578 scopus 로고    scopus 로고
    • Affine conjugate adaptive Newton methods for nonlinear elastomechanics
    • DOI 10.1080/10556780600605129, PII 773540732
    • WEISER, M., DEUFLHARD, P. & ERDMANN, B. (2007) Affine conjugate adaptive Newton methods for nonlinear elastomechanics. Optimization Methods and Software, 22, 413-431. (Pubitemid 46479850)
    • (2007) Optimization Methods and Software , 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.