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Volumn 107, Issue 3, 2006, Pages 409-438

Asymptotic behaviour of a family of gradient algorithms in ℝ d and Hilbert spaces

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL OPERATORS; MATHEMATICAL PROGRAMMING; OPTIMIZATION;

EID: 33645320243     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0602-7     Document Type: Article
Times cited : (10)

References (21)
  • 1
    • 0002662980 scopus 로고
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    • Akaike, H.: On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann. Inst. Statist. Math. Tokyo 11, 1-16 (1959)
    • (1959) Ann. Inst. Statist. Math. Tokyo , vol.11 , pp. 1-16
    • Akaike, H.1
  • 3
    • 0141467950 scopus 로고    scopus 로고
    • A spectral conjugate gradient method for unconstrained optimization
    • Birgin, E.G., Martínez, J.M.: A spectral conjugate gradient method for unconstrained optimization. Appl. Math. Optim. 43, 117-128 (2001)
    • (2001) Appl. Math. Optim. , vol.43 , pp. 117-128
    • Birgin, E.G.1    Martínez, J.M.2
  • 5
    • 0002034813 scopus 로고
    • On the asymptotic directions of the s-dimensional optimum gradient method
    • Forsythe, G.E.: On the asymptotic directions of the s-dimensional optimum gradient method. Numerische Mathematik 11, 57-76 (1968)
    • (1968) Numerische Mathematik , vol.11 , pp. 57-76
    • Forsythe, G.E.1
  • 8
    • 0001112787 scopus 로고
    • The equivalence of two extremum problems
    • Kiefer, J., Wolfowitz, J.: The equivalence of two extremum problems. Canadian J. Math. 12, 363-366 (1960)
    • (1960) Canadian J. Math. , vol.12 , pp. 363-366
    • Kiefer, J.1    Wolfowitz, J.2
  • 10
    • 0037861709 scopus 로고
    • An iteration process with minimal residues
    • Krasnosel'skii, M.A., Krein, S.G.: An iteration process with minimal residues. Mat. Sb. (in Russian) 31 (4), 315-334 (1952)
    • (1952) Mat. Sb. (in Russian) , vol.31 , Issue.4 , pp. 315-334
    • Krasnosel'skii, M.A.1    Krein, S.G.2
  • 13
    • 33645276063 scopus 로고    scopus 로고
    • On the accuracy of nonlinear optimization algorithms
    • ECE Department, Northwestern Univ., Evanston, II 60208
    • Nocedal, J., Sartenaer, A., Zhu, C.: On the accuracy of nonlinear optimization algorithms. Technical Report Nov. 1998, ECE Department, Northwestern Univ., Evanston, II 60208, 1998
    • (1998) Technical Report Nov. 1998
    • Nocedal, J.1    Sartenaer, A.2    Zhu, C.3
  • 16
    • 0035327288 scopus 로고    scopus 로고
    • Renormalised steepest descent in Hilbert space converges to a two-point attractor
    • Pronzato, L., Wynn, H.P., Zhigljavsky, A.A.: Renormalised steepest descent in Hilbert space converges to a two-point attractor. Acta Applicandae Mathematicae 67, 1-18 (2001)
    • (2001) Acta Applicandae Mathematicae , vol.67 , pp. 1-18
    • Pronzato, L.1    Wynn, H.P.2    Zhigljavsky, A.A.3
  • 18
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optimi. 7 (1), 26-33 (1997)
    • (1997) SIAM J. Optimi. , vol.7 , Issue.1 , pp. 26-33
    • Raydan, M.1
  • 19
    • 0036471006 scopus 로고    scopus 로고
    • Relaxed steepest descent and Cauchy-Barzilai-Borwein method
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.