메뉴 건너뛰기




Volumn 60, Issue 2, 2015, Pages 343-376

Algebraic rules for quadratic regularization of Newton’s method

Author keywords

Computational results; Global convergence; Local convergence; Newton s method; Regularization; Smooth unconstrained minimization

Indexed keywords

NEWTON-RAPHSON METHOD;

EID: 84924222053     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-014-9671-y     Document Type: Article
Times cited : (8)

References (25)
  • 1
    • 84868354042 scopus 로고    scopus 로고
    • Evaluating bound-constrained minimization software
    • Birgin, E.G., Gentil, J.M.: Evaluating bound-constrained minimization software. Comput. Optim. Appl. 53(2), 347–373 (2012)
    • (2012) Comput. Optim. Appl , vol.53 , Issue.2 , pp. 347-373
    • Birgin, E.G.1    Gentil, J.M.2
  • 2
    • 84859180670 scopus 로고    scopus 로고
    • Toint, Ph.L.: Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
    • Cartis, C., Gould, N.I.M., Toint, Ph.L.: Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Optim. Methods Softw. 27(2), 197–219 (2012)
    • (2012) Optim. Methods Softw , vol.27 , Issue.2 , pp. 197-219
    • Cartis, C.1    Gould, N.I.M.2
  • 3
    • 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(2), 245–295 (2011)
    • (2011) Math. Program , vol.127 , Issue.2 , pp. 245-295
    • Cartis, C.1    Gould, N.I.M.2
  • 4
    • 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(2), 295–319 (2011)
    • (2011) Math. Program , vol.130 , Issue.2 , pp. 295-319
    • Cartis, C.1    Gould, N.I.M.2
  • 6
    • 0003951723 scopus 로고    scopus 로고
    • Toint, Ph.L.: Trust-Region Methods. MPS/SIAM Series on Optimization. SIAM, Philadelphia
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods. MPS/SIAM Series on Optimization. SIAM, Philadelphia, PA (2000)
    • (2000) PA
    • Conn, A.R.1    Gould, N.I.M.2
  • 9
    • 84884286035 scopus 로고    scopus 로고
    • Descentwise inexact proximal algorithms for smooth optimization
    • Fuentes, M., Malick, J., Lemaréchal, C.: Descentwise inexact proximal algorithms for smooth optimization. Comput. Optim. Appl. 53(3), 755–769 (2012)
    • (2012) Comput. Optim. Appl , vol.53 , Issue.3 , pp. 755-769
    • Fuentes, M.1    Malick, J.2    Lemaréchal, C.3
  • 13
    • 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
  • 14
    • 38949178770 scopus 로고    scopus 로고
    • Self-adaptive inexact proximal point methods
    • Hager, W.W., Zhang, H.: Self-adaptive inexact proximal point methods. Comput. Optim. Appl. 39(2), 161–181 (2008)
    • (2008) Comput. Optim. Appl , vol.39 , Issue.2 , pp. 161-181
    • Hager, W.W.1    Zhang, H.2
  • 15
    • 0003894896 scopus 로고
    • An algorithm for minimization using exact second derivatives
    • AERE Harwell Laboratory, Harwell, Oxfordshire:
    • Hebden, M. D.: An algorithm for minimization using exact second derivatives. Technical Report T.P. 515, AERE Harwell Laboratory, Harwell, Oxfordshire (1973)
    • (1973) Technical Report T.P , vol.515
    • Hebden, M.D.1
  • 17
    • 0000873069 scopus 로고
    • A method for the solution of certain non-linear problems in least squares
    • Levenberg, K.: A method for the solution of certain non-linear problems in least squares. Quart. Appl. Math. 2, 164–168 (1944)
    • (1944) Quart. Appl. Math , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 18
    • 0001566816 scopus 로고
    • Régularisation d’inéquations variationnelles par approximations successives
    • Martinet, B.: Régularisation d’inéquations variationnelles par approximations successives. Rev. Française Info Recherche Opérationnelle, 4:154–158 (1970)
    • (1970) Rev. Française Info Recherche Opérationnelle , vol.4 , pp. 154-158
    • Martinet, B.1
  • 20
    • 33646730150 scopus 로고    scopus 로고
    • Cubic regularization of Newton method and its global performance
    • Nesterov, Y., Polyak, B. T.: Cubic regularization of Newton method and its global performance. Math. Program. 108(1):177–205 (2006)
    • (2006) Math. Program , vol.108 , Issue.1 , pp. 177-205
    • Nesterov, Y.1    Polyak, B.T.2
  • 22
    • 0022205528 scopus 로고
    • A modular system of algorithms for unconstrained minimization
    • Schnabel, R.B., Koontz, J.E., Weiss, B.E.: A modular system of algorithms for unconstrained minimization. ACM Trans. Math. Softw. 11(4), 419–440 (1985)
    • (1985) ACM Trans. Math. Softw , vol.11 , Issue.4 , pp. 419-440
    • Schnabel, R.B.1    Koontz, J.E.2    Weiss, B.E.3
  • 23
    • 84924221645 scopus 로고
    • On the stability of inverse problems (39
    • C. R. (Doklady) Acad. Sci. URSS (N.S, Moscow:
    • Tikhonov, A. N.: On the stability of inverse problems (39, pp. 176–179). C. R. (Doklady) Acad. Sci. URSS (N.S), Moscow (1943)
    • (1943) Pp , vol.176-179
    • Tikhonov, A.N.1
  • 25
    • 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.