메뉴 건너뛰기




Volumn 31, Issue 3, 1997, Pages 269-294

New convergence results on an algorithm for norm constrained regularization and related problems

Author keywords

Constrained Minimization; Fixed Point Quasi Newton methods; Ill Conditioning; Ill Posed Problems; Regularization; Trust region methods

Indexed keywords


EID: 0002185509     PISSN: 03990559     EISSN: None     Source Type: Journal    
DOI: 10.1051/ro/1997310302691     Document Type: Article
Times cited : (6)

References (26)
  • 1
    • 0002012034 scopus 로고
    • Generalization of the Wolfe reduced-gradient method to the case of nonlinear constraints
    • R. Fletcher (Ed.), Academic Press, London
    • J. ABADIE and J. CARPENTIER, Generalization of the Wolfe reduced-gradient method to the case of nonlinear constraints, in Optimization, R. Fletcher (Ed.), Academic Press, London, 1969.
    • (1969) Optimization
    • Abadie, J.1    Carpentier, J.2
  • 3
    • 0020099933 scopus 로고
    • On the local convergence of quasi-Newton methods for constrained optimization
    • P. T. BOGGS, J. W. TOLLE and P. WANG, On the local convergence of quasi-Newton methods for constrained optimization, SIAM Journal on Control and Optimization, 1982, 20, pp. 161-171.
    • (1982) SIAM Journal on Control and Optimization , vol.20 , pp. 161-171
    • Boggs, P.T.1    Tolle, J.W.2    Wang, P.3
  • 4
    • 0002336672 scopus 로고
    • A trust region strategy for nonlinear equality constrained optimization
    • (P. T. Boggs, R. Byrd and R. Schnabel, eds.), SIAM, Philadelphia
    • M. R. CELIS, J. E. DENNIS and R. A. TAPIA, A trust region strategy for nonlinear equality constrained optimization, in Numerical Optimization, (P. T. Boggs, R. Byrd and R. Schnabel, eds.), SIAM, Philadelphia, 1984, pp. 71-82.
    • (1984) Numerical Optimization , pp. 71-82
    • Celis, M.R.1    Dennis, J.E.2    Tapia, R.A.3
  • 5
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization with simple bounds
    • A. R. CONN, N. I. M. GOULD and Ph. L. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM Journal on Numerical Analysis, 1988, 25, pp. 433-460. See also SIAM Journal on Numerical Analysis, 1989, 26, pp. 764-767.
    • (1988) SIAM Journal on Numerical Analysis , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 6
    • 0001623391 scopus 로고
    • A. R. CONN, N. I. M. GOULD and Ph. L. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM Journal on Numerical Analysis, 1988, 25, pp. 433-460. See also SIAM Journal on Numerical Analysis, 1989, 26, pp. 764-767.
    • (1989) SIAM Journal on Numerical Analysis , vol.26 , pp. 764-767
  • 7
    • 0026104343 scopus 로고
    • A global convergence theory for the Celis-Dennis-Tapia trust region algorithm for constrained optimization
    • M. M. EL-ALEM, A global convergence theory for the Celis-Dennis-Tapia trust region algorithm for constrained optimization, SIAM Journal on Numerical Analysis, 1991, 28, pp. 266-290.
    • (1991) SIAM Journal on Numerical Analysis , vol.28 , pp. 266-290
    • El-Alem, M.M.1
  • 10
    • 0000955796 scopus 로고
    • Computing optimal locally constrained steps
    • D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sci. Stat. Comput., 1981, 2, pp. 186-197.
    • (1981) SIAM J. Sci. Stat. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 11
    • 0000409919 scopus 로고
    • Mesh independence for nonlinear least squares problems with norm constraints
    • M. HEINKENSCHLOSS, Mesh independence for nonlinear least squares problems with norm constraints, SIAM Journal on Optimization, 1993, 3, pp. 81-117.
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 81-117
    • Heinkenschloss, M.1
  • 12
    • 0003379153 scopus 로고
    • Reduced gradient methods
    • edited by M. J. D. Powell, Academic Press, New York
    • L. S. LASDON, Reduced gradient methods, in Nonlinear Optimization 1981, 1982, edited by M. J. D. Powell, Academic Press, New York, pp. 235-242.
    • (1982) Nonlinear Optimization 1981 , pp. 235-242
    • Lasdon, L.S.1
  • 15
    • 0026941648 scopus 로고
    • Fixed-point quasi-Newton methods, SIAM
    • J. M. MARTÍNEZ, Fixed-point quasi-Newton methods, SIAM Journal on Numerical Analysis, 1992, 5, pp. 1413-1434.
    • (1992) Journal on Numerical Analysis , vol.5 , pp. 1413-1434
    • Martínez, J.M.1
  • 16
    • 0000442245 scopus 로고
    • Local minimizers of quadratic functions on Euclidean balls and spheres
    • J. M. MARTÍNEZ, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM Journal on Optimization, 1994, 4, pp. 159-176.
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 159-176
    • Martínez, J.M.1
  • 17
    • 34249768673 scopus 로고
    • A trust-region strategy for minimization on arbitrary domains
    • J. M. MARTINEZ and S. A. SANTOS, A trust-region strategy for minimization on arbitrary domains, Mathematical Programming, 1995, 68, pp. 267-301.
    • (1995) Mathematical Programming , vol.68 , pp. 267-301
    • Martinez, J.M.1    Santos, S.A.2
  • 18
    • 0003162836 scopus 로고
    • Recent developments in algorithms and software for trust region methods
    • A. Bachem, M Grötschel and B. Korte, eds., Springer-Verlag
    • J. J. MORÉ, Recent developments in algorithms and software for trust region methods, in Mathematical Programming Bonn 1982. The State of Art, A. Bachem, M Grötschel and B. Korte, eds., Springer-Verlag, 1983.
    • (1983) Mathematical Programming Bonn 1982. The State of Art
    • Moré, J.J.1
  • 19
    • 0027901827 scopus 로고
    • Generalizations of the trust-region Problem
    • J. J. MORÉ, Generalizations of the trust-region Problem, Optimization Methods and Software, 1993, 2, pp. 189-209.
    • (1993) Optimization Methods and Software , vol.2 , pp. 189-209
    • Moré, J.J.1
  • 21
    • 34249955300 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • M. J. D. POWELL and Y. YUAN, A trust region algorithm for equality constrained optimization, Mathematical Programming, 1991, 49, pp. 189-211.
    • (1991) Mathematical Programming , vol.49 , pp. 189-211
    • Powell, M.J.D.1    Yuan, Y.2
  • 22
    • 0010763968 scopus 로고
    • Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations
    • School of Engineering and Applied Science, Department of Civil Engineering and Operations Research, Princeton University
    • R. J. STERN and H. WOLKOWICZ, Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations, Technical Report SOR 93-1, School of Engineering and Applied Science, Department of Civil Engineering and Operations Research, Princeton University, 1993.
    • (1993) Technical Report SOR 93-1
    • Stern, R.J.1    Wolkowicz, H.2
  • 23
    • 0001382978 scopus 로고
    • Newton's method with a model trust region modification
    • D. C. SORENSEN, Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis, 1982, 19, pp. 409-426.
    • (1982) SIAM Journal on Numerical Analysis , vol.19 , pp. 409-426
    • Sorensen, D.C.1
  • 25
    • 0025249660 scopus 로고
    • A constrained least-squares regularization method for nonlinear ill-posed problems
    • C. R. VOGEL, A constrained least-squares regularization method for nonlinear ill-posed problems, SIAM Journal on Control and Optimization, 1990, 28, pp. 34-49.
    • (1990) SIAM Journal on Control and Optimization , vol.28 , pp. 34-49
    • Vogel, C.R.1
  • 26
    • 85033318647 scopus 로고
    • On the resolution of the trust region problem
    • Communication Il Ciocco, Italy, September 1993
    • H. WOLKOWICZ, On the resolution of the trust region problem, Communication at the NATO-ASI Meeting on Continuous Optimization, Il Ciocco, Italy, September 1993, 1993.
    • (1993) NATO-ASI Meeting on Continuous Optimization
    • Wolkowicz, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.