메뉴 건너뛰기




Volumn 25, Issue 2, 2005, Pages 221-252

Spectral projected gradient and variable metric methods for optimization with linear inequalities

Author keywords

Linearly constrained optimization; Non monotonic line search; Projected gradient; Spectral gradient

Indexed keywords

ITERATIVE METHODS; QUADRATIC PROGRAMMING;

EID: 25844440817     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drh020     Document Type: Article
Times cited : (14)

References (43)
  • 1
    • 0001531895 scopus 로고
    • Two point step size gradient methods
    • BARZILAI, J. & BORWEIN, J. M. (1988) Two point step size gradient methods. IMA J. Numer. Anal., 8, 141-148.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 141-148
    • Barzilai, J.1    Borwein, J.M.2
  • 3
    • 0016948909 scopus 로고
    • On the Goldstein-levitin-polyak gradient projection method
    • BERTSEKAS, D. P. (1976) On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Automat. Control, 21, 174-184.
    • (1976) IEEE Trans. Automat. Control , vol.21 , pp. 174-184
    • Bertsekas, D.P.1
  • 5
    • 0036794059 scopus 로고    scopus 로고
    • Large-scale active-set box-constrained optimization method with spectral projected gradients
    • BIRGIN, E. G. & MARTÍNEZ, J. M. (2002) Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl., 23, 101-125.
    • (2002) Comput. Optim. Appl. , vol.23 , pp. 101-125
    • Birgin, E.G.1    Martínez, J.M.2
  • 6
    • 0034345420 scopus 로고    scopus 로고
    • Nonmonotone spectral projected gradient methods on convex sets
    • BIRGIN, E. G., MARTÍNEZ, J. M. & RAYDAN, M. (2000) Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim., 10, 1196-1211.
    • (2000) SIAM J. Optim. , vol.10 , pp. 1196-1211
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 7
    • 18044400238 scopus 로고    scopus 로고
    • Algorithm 813: SPG - Software for convex-constrained optimization
    • BIRGIN, E. G., MARTÍNEZ, J. M. & RAYDAN, M. (2001) Algorithm 813: SPG - software for convex-constrained optimization. ACM Trans. Math. Softw., 27, 340-349.
    • (2001) ACM Trans. Math. Softw. , vol.27 , pp. 340-349
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 8
    • 0142199775 scopus 로고    scopus 로고
    • Inexact spectral projected gradient methods on convex sets
    • BIRGIN, E. G., MARTÍNEZ, J. M. & RAYDAN, M. (2003) Inexact spectral projected gradient methods on convex sets. IMA J. Numer. Anal., 23, 539-559.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 539-559
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 10
    • 0002436271 scopus 로고
    • A method for finding projections onto the intersection of convex sets in Hilbert spaces
    • BOYLE, J. P. & DYKSTRA, R. L. (1986) A method for finding projections onto the intersection of convex sets in Hilbert spaces. Lecture Notes in Statistics, 37, 28-47.
    • (1986) Lecture Notes in Statistics , vol.37 , pp. 28-47
    • Boyle, J.P.1    Dykstra, R.L.2
  • 11
    • 1642543147 scopus 로고    scopus 로고
    • A limited memory multipoint secant method for bound constrained optimization
    • BURDAKOV, O., MARTÍNEZ, J. M. & PILOTTA, E. A. (2002) A limited memory multipoint secant method for bound constrained optimization. Ann. Oper. Res., 117, 51-70.
    • (2002) Ann. Oper. Res. , vol.117 , pp. 51-70
    • Burdakov, O.1    Martínez, J.M.2    Pilotta, E.A.3
  • 12
    • 0023416451 scopus 로고
    • Projected gradient methods for linearly constrained problems
    • CALAMAI, P. H. & MORÉ, J. J. (1987) Projected gradient methods for linearly constrained problems. Math. Programm., 39, 93-116.
    • (1987) Math. Programm. , vol.39 , pp. 93-116
    • Calamai, P.H.1    Moré, J.J.2
  • 14
    • 0036112899 scopus 로고    scopus 로고
    • On the nonmonotone line search
    • DAI, Y. H. (2002) On the nonmonotone line search. J. Optim. Theory Appl., 112, 315-330.
    • (2002) J. Optim. Theory Appl. , vol.112 , pp. 315-330
    • Dai, Y.H.1
  • 15
    • 0036102376 scopus 로고    scopus 로고
    • R-linear convergence of the Barzilai and Borwein gradient method
    • DAI, Y. H. & LIAO, L. Z. (2002) R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal., 22, 1-10.
    • (2002) IMA J. Numer. Anal. , vol.22 , pp. 1-10
    • Dai, Y.H.1    Liao, L.Z.2
  • 16
    • 84966259557 scopus 로고
    • A characterization of superlinear convergence and its application to quasi-Newton methods
    • DENNIS JR., J. E. & MORÉ, J. J. (1974) A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comput., 28, 549-560.
    • (1974) Math. Comput. , vol.28 , pp. 549-560
    • Dennis Jr., J.E.1    Moré, J.J.2
  • 18
    • 0031285901 scopus 로고    scopus 로고
    • Box constrained quadratic programming with proportioning and projections
    • DOSTÁL, Z. (1997) Box constrained quadratic programming with proportioning and projections. SIAM J. Optim., 7, 871-887.
    • (1997) SIAM J. Optim. , vol.7 , pp. 871-887
    • Dostál, Z.1
  • 19
    • 84948499836 scopus 로고
    • An algorithm for restricted least-squares regression
    • DYKSTRA, R. L. (1983) An algorithm for restricted least-squares regression. J. Am. Statist. Assoc., 78, 837-842.
    • (1983) J. Am. Statist. Assoc. , vol.78 , pp. 837-842
    • Dykstra, R.L.1
  • 20
    • 0026215819 scopus 로고
    • Algorithm 695 - Software for a new modified Cholesky factorization
    • ESKOW, E. & SCHNABEL, R. B. (1991) Algorithm 695 - software for a new modified Cholesky factorization. ACM Trans. Math. Softw., 17, 306-312.
    • (1991) ACM Trans. Math. Softw. , vol.17 , pp. 306-312
    • Eskow, E.1    Schnabel, R.B.2
  • 21
    • 25844452827 scopus 로고    scopus 로고
    • FAN, M. (2000) http://www.aemdesign.com/.
    • (2000)
    • Fan, M.1
  • 24
    • 0011768018 scopus 로고    scopus 로고
    • Report NA/207 Department of Mathematics, University of Dundee
    • FLETCHER, R. (2001) On the Barzilai-Borwein method. Report NA/207 Department of Mathematics, University of Dundee.
    • (2001) On the Barzilai-borwein Method
    • Fletcher, R.1
  • 25
    • 0000064079 scopus 로고
    • On the maximization of a concave quadratic function with box constraints
    • FRIEDLANDER, A. & MARTÍNEZ, J. M. (1994) On the maximization of a concave quadratic function with box constraints. SIAM J. Optim., 4, 177-192.
    • (1994) SIAM J. Optim. , vol.4 , pp. 177-192
    • Friedlander, A.1    Martínez, J.M.2
  • 26
    • 0029424630 scopus 로고
    • A new method for large-scale box constrained convex quadratic minimization problems
    • FRIEDLANDER, A., MARTÍNEZ, J. M. & RAYDAN, M. (1995) A new method for large-scale box constrained convex quadratic minimization problems. Optim. Methods Softw., 5, 57-74.
    • (1995) Optim. Methods Softw. , vol.5 , pp. 57-74
    • Friedlander, A.1    Martínez, J.M.2    Raydan, M.3
  • 27
    • 0001673058 scopus 로고
    • A necessary and sufficient condition to have bounded multipliers in nonconvex programming
    • GAUVIN, J. (1977) A necessary and sufficient condition to have bounded multipliers in nonconvex programming. Math. Programm., 12, 136-138.
    • (1977) Math. Programm. , vol.12 , pp. 136-138
    • Gauvin, J.1
  • 29
    • 84966240089 scopus 로고
    • Convex programming in Hilbert space
    • GOLDSTEIN, A. A. (1964) Convex programming in Hilbert space. Bull. Am. Math. Soc., 70, 709-710.
    • (1964) Bull. Am. Math. Soc. , vol.70 , pp. 709-710
    • Goldstein, A.A.1
  • 30
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • GRIPPO, L., LAMPARIELLO, F. & LUCIDI, S. (1986) A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal., 23, 707-716.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 31
    • 0023860607 scopus 로고
    • A successive projection method
    • HAN, S. P. (1988) A successive projection method. Math. Programm., 40, 1-14.
    • (1988) Math. Programm. , vol.40 , pp. 1-14
    • Han, S.P.1
  • 34
    • 0017908843 scopus 로고
    • Large-scale linearly constrained optimization
    • MURTAGH, B. A. & SAUNDERS, M. A. (1978) Large-scale linearly constrained optimization. Math. Programm., 14, 41-72.
    • (1978) Math. Programm. , vol.14 , pp. 41-72
    • Murtagh, B.A.1    Saunders, M.A.2
  • 35
    • 0027578884 scopus 로고
    • On combining feasibility, descent and superlinear convergence in inequality constrained optimization
    • PANIER, E. & TITS, A. L. (1993) On combining feasibility, descent and superlinear convergence in inequality constrained optimization. Math. Programm., 59, 261-276.
    • (1993) Math. Programm. , vol.59 , pp. 261-276
    • Panier, E.1    Tits, A.L.2
  • 36
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein choice of steplength for the gradient method
    • RAYDAN, M. (1993) On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal., 13, 321-326.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 37
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • RAYDAN, M. (1997) The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim., 7, 26-33.
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 38
    • 0043184621 scopus 로고    scopus 로고
    • Primal and polar approach for computing the symmetric diagonally dominant projection
    • RAYDAN, M. & TARAZAGA, P. (2002) Primal and polar approach for computing the symmetric diagonally dominant projection. Numer. Linear Algebra Appl., 9, 333-345.
    • (2002) Numer. Linear Algebra Appl. , vol.9 , pp. 333-345
    • Raydan, M.1    Tarazaga, P.2
  • 39
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • ROCKAFELLAR, R. T. (1976) Monotone operators and the proximal point algorithm. SIAM J. Control Optim., 14, 877-898.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 40
    • 0033293912 scopus 로고    scopus 로고
    • An interior point code for quadratic programming
    • VANDERBEI, R. J. (1999) An interior point code for quadratic programming. Optim. Methods Softw., 12, 451-484.
    • (1999) Optim. Methods Softw. , vol.12 , pp. 451-484
    • Vanderbei, R.J.1
  • 41
    • 0000287204 scopus 로고    scopus 로고
    • An interior point algorithm for nonconvex nonlinear programming
    • VANDERBEI, R. J. & SHANNO, D. F. (1999) An interior point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl., 13, 231-252.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 231-252
    • Vanderbei, R.J.1    Shanno, D.F.2
  • 42
    • 0027561173 scopus 로고
    • Nonmonotone line search for minimax problems
    • ZHOU, J. L. & TITS, A. L. (1993) Nonmonotone line search for minimax problems. J. Optim. Theory Appl., 76, 455-476.
    • (1993) J. Optim. Theory Appl. , vol.76 , pp. 455-476
    • Zhou, J.L.1    Tits, A.L.2
  • 43
    • 0003997741 scopus 로고    scopus 로고
    • User's Guide for FFSQP Version 3.7: A Fortran code for solving optimization programs, possibly minimax, with general inequality constraints and linear equality constraints, generating feasible iterates
    • Institute for Systems Research, University of Maryland
    • ZHOU, J. L. & TITS, A. (1997) User's Guide for FFSQP Version 3.7: A Fortran code for solving optimization programs, possibly minimax, with general inequality constraints and linear equality constraints, generating feasible iterates. Technical Report SRC-TR-92-107r5 Institute for Systems Research, University of Maryland.
    • (1997) Technical Report , vol.SRC-TR-92-107R5
    • Zhou, J.L.1    Tits, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.