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Volumn 135, Issue 1-2, 2012, Pages 413-436

A limited memory steepest descent method

Author keywords

65K05; 90C26; Mathematics Subject Classification (2000): 90C06

Indexed keywords

65K05; 90C26; LANCZOS; LANCZOS PROCESS; LARGE DIMENSIONS; LIMITED MEMORY; LIMITED-MEMORY METHODS; NUMERICAL EVIDENCE; OBJECTIVE FUNCTIONS; RITZ VALUES; STATE OF THE ART; STEP SIZE; SUBJECT CLASSIFICATION; UNCONSTRAINED MINIMIZATION PROBLEM;

EID: 84866235041     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0479-6     Document Type: Article
Times cited : (63)

References (26)
  • 1
    • 0001531895 scopus 로고
    • Two-point step size gradient methods
    • 967848 0638.65055 10.1093/imanum/8.1.141
    • Barzilai J., Borwein J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141-148 (1988)
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 141-148
    • Barzilai, J.1    Borwein, J.M.2
  • 2
    • 0028319529 scopus 로고
    • Representations of Quasi-Newton matrices and their use in limited memory methods
    • 1268604 0809.90116 10.1007/BF01582063
    • Byrd R.H., Nocedal J., Schnabel R.B.: Representations of Quasi-Newton matrices and their use in limited memory methods. Math. Progr. 63, 129-156 (1994)
    • (1994) Math. Progr. , vol.63 , pp. 129-156
    • Byrd, R.H.1    Nocedal, J.2    Schnabel, R.B.3
  • 3
    • 0000478038 scopus 로고
    • Méthode générale pour la résolution des systèms d'équations simultanées
    • Cauchy A.: Méthode générale pour la résolution des systèms d'équations simultanées. Comp. Rend. Sci. Paris 25, 536-538 (1847)
    • (1847) Comp. Rend. Sci. Paris , vol.25 , pp. 536-538
    • Cauchy, A.1
  • 4
    • 21644488546 scopus 로고    scopus 로고
    • On the asymptotic behaviour of some new gradient methods
    • 2166548 1099.90038 10.1007/s10107-004-0516-9
    • Dai Y.H., Fletcher R.: On the asymptotic behaviour of some new gradient methods. Math. Progr. 103, 541-559 (2005)
    • (2005) Math. Progr. , vol.103 , pp. 541-559
    • Dai, Y.H.1    Fletcher, R.2
  • 5
    • 15544385032 scopus 로고    scopus 로고
    • Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
    • 2129700 1068.65073 10.1007/s00211-004-0569-y
    • Dai Y.H., Fletcher R.: Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming. Numer. Math. 100, 21-47 (2005)
    • (2005) Numer. Math. , vol.100 , pp. 21-47
    • Dai, Y.H.1    Fletcher, R.2
  • 6
    • 46249097121 scopus 로고    scopus 로고
    • Analysis of monotone gradient methods
    • 2136784 1071.65084 10.3934/jimo.2005.1.181
    • Dai Y.H., Yuan Y.: Analysis of monotone gradient methods. J. Ind. Manag. Optim. 1, 181-192 (2005)
    • (2005) J. Ind. Manag. Optim. , vol.1 , pp. 181-192
    • Dai, Y.H.1    Yuan, Y.2
  • 10
    • 0000387235 scopus 로고
    • A rapidly convergent descent method for minimization
    • 152116 0132.11603
    • Fletcher R., Powell M.J.D.: A rapidly convergent descent method for minimization. Comput. J. 6, 163-168 (1963)
    • (1963) Comput. J. , vol.6 , pp. 163-168
    • Fletcher, R.1    Powell, M.J.D.2
  • 13
    • 2442598318 scopus 로고    scopus 로고
    • CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited
    • 2077337 1068.90526 10.1145/962437.962439
    • Gould N.I.M., Orban D., Toint Ph.L.: CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 373-394 (2003)
    • (2003) ACM Trans. Math. Softw. , vol.29 , pp. 373-394
    • Gould, N.I.M.1    Orban, D.2    Toint, Ph.L.3
  • 14
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • 849278 0616.65067 10.1137/0723046
    • Grippo L., Lampariello F., Lucidi S.: A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal. 23, 707-716 (1986)
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 15
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • 42791 10.6028/jres.045.026
    • Lanczos C.: An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Stand. 45, 255-282 (1950)
    • (1950) J. Res. Nat. Bur. Stand. , vol.45 , pp. 255-282
    • Lanczos, C.1
  • 16
    • 21444432174 scopus 로고    scopus 로고
    • Preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations
    • 1417682 0861.65025 10.1007/BF02143126
    • Molina B., Raydan M.: Preconditioned Barzilai-Borwein method for the numerical solution of partial differential equations. Numer. Algoritm. 13, 45-60 (1996)
    • (1996) Numer. Algoritm. , vol.13 , pp. 45-60
    • Molina, B.1    Raydan, M.2
  • 17
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • 572855 0464.65037 10.1090/S0025-5718-1980-0572855-7
    • Nocedal J.: Updating quasi-Newton matrices with limited storage. Math. Comput. 35, 773-782 (1980)
    • (1980) Math. Comput. , vol.35 , pp. 773-782
    • Nocedal, J.1
  • 18
    • 84985350406 scopus 로고
    • Approximate solutions and eigenvalue bounds from Krylov subspaces
    • 1323816 0831.65036 10.1002/nla.1680020205
    • Paige C.C., Parlett B.N., van der Vorst H.: Approximate solutions and eigenvalue bounds from Krylov subspaces. Numer. Linear Algebra Appl. 2, 115-133 (1995)
    • (1995) Numer. Linear Algebra Appl. , vol.2 , pp. 115-133
    • Paige, C.C.1    Parlett, B.N.2    Van Der Vorst, H.3
  • 19
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein choice of steplength for the gradient method
    • 1225468 0778.65045 10.1093/imanum/13.3.321
    • Raydan M.: On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13, 321-326 (1993)
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 20
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • 1430555 0898.90119 10.1137/S1052623494266365
    • Raydan M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7, 26-33 (1997)
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 21
    • 0036471006 scopus 로고    scopus 로고
    • Relaxed steepest descent and Cauchy-Barzilai-Borwein method
    • 1883751 0988.90049 10.1023/A:1013708715892
    • Raydan M., Svaiter B.F.: Relaxed steepest descent and Cauchy-Barzilai-Borwein method. Comput. Optim. Appl. 21, 155-167 (2002)
    • (2002) Comput. Optim. Appl. , vol.21 , pp. 155-167
    • Raydan, M.1    Svaiter, B.F.2
  • 22
    • 12444278992 scopus 로고    scopus 로고
    • Gradient projection methods for quadratic programs and applications in support vector machines
    • 2141838 1072.90026 10.1080/10556780512331318182
    • Serafini T., Zanghirati G., Zanni L.: Gradient projection methods for quadratic programs and applications in support vector machines. Optim. Methods Softw. 20, 353-378 (2005)
    • (2005) Optim. Methods Softw. , vol.20 , pp. 353-378
    • Serafini, T.1    Zanghirati, G.2    Zanni, L.3
  • 23
    • 84966243875 scopus 로고
    • Some numerical results using a sparse matrix updating formula in unconstrained optimization
    • 483452 0381.65036 10.1090/S0025-5718-1978-0483452-7
    • Toint Ph.L.: Some numerical results using a sparse matrix updating formula in unconstrained optimization. Math. Comput. 32, 839-852 (1978)
    • (1978) Math. Comput. , vol.32 , pp. 839-852
    • Toint, Ph.L.1
  • 24
    • 70350426511 scopus 로고    scopus 로고
    • BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function
    • Varadhan R., Gilbert P.D.: BB: an R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. J. Stat. Softw. 32, 1-26 (2009)
    • (2009) J. Stat. Softw. , vol.32 , pp. 1-26
    • Varadhan, R.1    Gilbert, P.D.2
  • 25
    • 0037415945 scopus 로고    scopus 로고
    • Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method
    • 10.1016/S0040-6090(02)01117-3
    • Vargas W.E., Azofeifa D.E., Clark N.: Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method. Thin Solid Films 425, 1-8 (2003)
    • (2003) Thin Solid Films , vol.425 , pp. 1-8
    • Vargas, W.E.1    Azofeifa, D.E.2    Clark, N.3
  • 26
    • 33645651209 scopus 로고    scopus 로고
    • A new stepsize for the steepest descent method
    • 2204453 1101.65067
    • Yuan Y.: A new stepsize for the steepest descent method. J. Comput. Math. 24, 149-156 (2006)
    • (2006) J. Comput. Math. , vol.24 , pp. 149-156
    • Yuan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.