메뉴 건너뛰기




Volumn 20, Issue 6, 2005, Pages 693-713

Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization

Author keywords

Conjugate gradient (CG) method; Equilibrated matrix; Preconditioning; Row column scaling; Truncated Newton method

Indexed keywords

ALGORITHMS; LINEAR SYSTEMS; MATRIX ALGEBRA; OPTIMIZATION; VECTORS;

EID: 29744436841     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780410001727709     Document Type: Article
Times cited : (10)

References (37)
  • 1
    • 0039169768 scopus 로고    scopus 로고
    • Large scale unconstrained optimization
    • A. Watson and I. Duff (Eds) (Oxford: Oxford University Press)
    • Nocedal, J., 1997, Large scale unconstrained optimization. In: A. Watson and I. Duff (Eds) The State of the Art in Numerical Analysis (Oxford: Oxford University Press), pp. 311-338.
    • (1997) The State of the Art in Numerical Analysis , pp. 311-338
    • Nocedal, J.1
  • 2
    • 29744453893 scopus 로고    scopus 로고
    • Large scale unconstrained optimization
    • C. Floudas and P. Pardalos (Eds) (Kluwer Academic Publishers)
    • Roma, M., 2001, Large scale unconstrained optimization. In: C. Floudas and P. Pardalos (Eds) Encyclopedia of Optimization, Vol. III (Kluwer Academic Publishers), pp. 143-150.
    • (2001) Encyclopedia of Optimization , vol.3 , pp. 143-150
    • Roma, M.1
  • 4
    • 0020129823 scopus 로고
    • A discrete Newton algorithm for minimizing a function of many variables
    • O'Leary, D.P., 1982, A discrete Newton algorithm for minimizing a function of many variables. Mathematical Programming, 23, 20-33.
    • (1982) Mathematical Programming , vol.23 , pp. 20-33
    • O'Leary, D.P.1
  • 5
    • 0034345411 scopus 로고    scopus 로고
    • Automatic preconditioning by limited memory quasi-Newton updating
    • Morales, J.L. and Nocedal, J., 2000, Automatic preconditioning by limited memory quasi-Newton updating. SIAM Journal on Optimization, 10, 1079-1096.
    • (2000) SIAM Journal on Optimization , vol.10 , pp. 1079-1096
    • Morales, J.L.1    Nocedal, J.2
  • 6
    • 0002090018 scopus 로고
    • Condition number and equilibration of matrices
    • Van der Sluis, A., 1969, Condition number and equilibration of matrices. Numerische Mathematik, 14, 14-23.
    • (1969) Numerische Mathematik , vol.14 , pp. 14-23
    • Van Der Sluis, A.1
  • 7
    • 0002122998 scopus 로고
    • Optimally scaled matrices
    • Bauer, F.L., 1963, Optimally scaled matrices. Numerische Mathematik, 5, 73-87.
    • (1963) Numerische Mathematik , vol.5 , pp. 73-87
    • Bauer, F.L.1
  • 10
    • 0020763823 scopus 로고
    • Truncated-Newton algorithms for large-scale unconstrained optimization
    • Dembo, R.S. and Steihaug, T., 1983, Truncated-Newton algorithms for large-scale unconstrained optimization. Mathematical Programming, 26, 190-212.
    • (1983) Mathematical Programming , vol.26 , pp. 190-212
    • Dembo, R.S.1    Steihaug, T.2
  • 18
    • 0033294627 scopus 로고    scopus 로고
    • Incomplete Cholesky factorization with limited memory
    • Lin, C.-J. and Moré, J., 1999, Incomplete Cholesky factorization with limited memory. SIAM Journal on Scientific Computing, 21, 24-45.
    • (1999) SIAM Journal on Scientific Computing , vol.21 , pp. 24-45
    • Lin, C.-J.1    Moré, J.2
  • 19
    • 0001347358 scopus 로고
    • Modified Cholesky factorization for sparse preconditioners
    • Schlick, T., 1993, Modified Cholesky factorization for sparse preconditioners. SIAM Journal on Scientific Computing, 14, 424-445.
    • (1993) SIAM Journal on Scientific Computing , vol.14 , pp. 424-445
    • Schlick, T.1
  • 20
    • 0040845777 scopus 로고    scopus 로고
    • Preconditioning Newton's method
    • Center for Research on Parallel Computing, Rice University, Houston, TX
    • Bouaricha, A., Moré, J. and Wu, Z., 1998, Preconditioning Newton's method. Technical Report CRPC-TR98762, Center for Research on Parallel Computing, Rice University, Houston, TX.
    • (1998) Technical Report , vol.CRPC-TR98762
    • Bouaricha, A.1    Moré, J.2    Wu, Z.3
  • 21
    • 0031261356 scopus 로고    scopus 로고
    • Element-by-element preconditioners for large-scale partially separable optimization problems
    • Daydé, M.J., L'Excellent, J.-Y. and Gould, N.I.M., 1997, Element-by-element preconditioners for large-scale partially separable optimization problems. SIAM Journal on Scientific Computing, 18, 1767-1787.
    • (1997) SIAM Journal on Scientific Computing , vol.18 , pp. 1767-1787
    • Daydé, M.J.1    L'Excellent, J.-Y.2    Gould, N.I.M.3
  • 22
    • 0003086453 scopus 로고
    • On automatic differentiation
    • M. Iri and K. Tanake (Eds) (Kluwer Academic Publishers)
    • Griewank, A., 1989, On automatic differentiation. In: M. Iri and K. Tanake (Eds) Mathematical Programming: Recent Developments and Applications (Kluwer Academic Publishers), pp. 83-108.
    • (1989) Mathematical Programming: Recent Developments and Applications , pp. 83-108
    • Griewank, A.1
  • 24
    • 0001684438 scopus 로고
    • A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization
    • Nash, S.G. and Nocedal, J., 1991, A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization. SIAM Journal on Optimization, 1, 358-372.
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 358-372
    • Nash, S.G.1    Nocedal, J.2
  • 25
    • 0011630080 scopus 로고    scopus 로고
    • Algorithm PREQN: Fortran 77 subroutine for preconditioning the conjugate gradient method
    • Morales, J.L. and Nocedal, J., 2001, Algorithm PREQN: Fortran 77 subroutine for preconditioning the conjugate gradient method. ACM Transaction on Mathematical Software, 27, 83-91.
    • (2001) ACM Transaction on Mathematical Software , vol.27 , pp. 83-91
    • Morales, J.L.1    Nocedal, J.2
  • 27
    • 0025432633 scopus 로고
    • A comparative study of algorithms for matrix balancing
    • Schneider, M.H. and Zenios, S., 1990, A comparative study of algorithms for matrix balancing. Operations Research, 38, 439-455.
    • (1990) Operations Research , vol.38 , pp. 439-455
    • Schneider, M.H.1    Zenios, S.2
  • 28
    • 29744443277 scopus 로고    scopus 로고
    • A scaling algorithm to equilibrate both rows and columns norms in matrices
    • Computational Sciences and Engineering Department, Rutherford Appleton Laboratory, Oxon, UK. (Submitted to Linear Algebra and Applications.)
    • Ruiz, D., 2001, A scaling algorithm to equilibrate both rows and columns norms in matrices. Technical Report RAL-TR-2001-034, Computational Sciences and Engineering Department, Rutherford Appleton Laboratory, Oxon, UK. (Submitted to Linear Algebra and Applications.)
    • (2001) Technical Report , vol.RAL-TR-2001-034
    • Ruiz, D.1
  • 29
    • 84976691565 scopus 로고
    • Equilibration of symmetric matrices in the max-norm
    • Bunch, J.R., 1971, Equilibration of symmetric matrices in the max-norm. Journal of ACM, 18, 566-572.
    • (1971) Journal of ACM , vol.18 , pp. 566-572
    • Bunch, J.R.1
  • 32
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization
    • Liu, D.C. and Nocedal, J., 1989, On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 503-528.
    • (1989) Mathematical Programming , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 33
    • 0013358480 scopus 로고
    • Partitioned variable metric updates for large structured optimization problems
    • Griewank, A. and Toint, Ph.L., 1982, Partitioned variable metric updates for large structured optimization problems. Numerische Mathematik, 39, 119-137.
    • (1982) Numerische Mathematik , vol.39 , pp. 119-137
    • Griewank, A.1    Toint, Ph.L.2
  • 34
    • 0029425799 scopus 로고
    • The effect of diagonal scaling on projected gradient methods for bound constrained quadratic programming problems
    • Barlow, J.L. and Toraldo, G., 1995, The effect of diagonal scaling on projected gradient methods for bound constrained quadratic programming problems. Optimization Methods and Software, 5, 235-245.
    • (1995) Optimization Methods and Software , vol.5 , pp. 235-245
    • Barlow, J.L.1    Toraldo, G.2
  • 35
    • 0025463531 scopus 로고
    • Assessing a search direction within a truncated-Newton method
    • Nash, S.G. and Sofer, A., 1990, Assessing a search direction within a truncated-Newton method. Operations Research Letter, 9, 219-221.
    • (1990) Operations Research Letter , vol.9 , pp. 219-221
    • Nash, S.G.1    Sofer, A.2
  • 36
    • 29744465289 scopus 로고    scopus 로고
    • Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization: The complete results
    • IASI-CNR. Revised 2003
    • Roma, M., 2002, Dynamic scaling based preconditioning for truncated Newton methods in large scale unconstrained optimization: the complete results. Technical Report R. 579, IASI-CNR. Revised 2003. Available at http://www.dis.uniroma1.it/~roma/R579.pdf.
    • (2002) Technical Report , vol.R. 579
    • Roma, M.1
  • 37
    • 0034560396 scopus 로고    scopus 로고
    • Adaptative use of iterative methods in predictor-corrector interior point methods for linear programming
    • Wang, W. and O'Leary, D.P., 2000, Adaptative use of iterative methods in predictor-corrector interior point methods for linear programming. Numerical Algorithms, 25, 387-406.
    • (2000) Numerical Algorithms , vol.25 , pp. 387-406
    • Wang, W.1    O'Leary, D.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.