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Volumn 58, Issue 2, 2008, Pages 275-290

Subspace Barzilai-Borwein gradient method for large-scale bound constrained optimization

Author keywords

Barzilai Borwein gradient method; Bound constrained problem; Nonmonotone line search; Stationary point

Indexed keywords

ACTIVE SET; BARZILAI-BORWEIN GRADIENT METHOD; BOUND CONSTRAINED OPTIMIZATION; BOUND CONSTRAINED PROBLEM; CONSTRAINED PROBLEMS; GLOBAL CONVERGENCE; GRADIENT ALGORITHMS; IDENTIFICATION TECHNIQUES; NONMONOTONE LINE SEARCH; NUMERICA L RESULTS; SEARCH DIRECTION; STATIONARY POINT;

EID: 51849107311     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-008-9038-9     Document Type: Article
Times cited : (19)

References (34)
  • 1
    • 45849133389 scopus 로고    scopus 로고
    • On augmented Lagrangian methods with general lower-level constraints
    • Andreani, R., Birgin, E.G., Martínez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18, 1286-1309 (2007)
    • (2007) SIAM J. Optim. , vol.18 , pp. 1286-1309
    • Andreani, R.1    Birgin, E.G.2    Martínez, J.M.3    Schuverdt, M.L.4
  • 2
    • 34347264176 scopus 로고    scopus 로고
    • Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
    • Andreani, R., Birgin, E.G., Martínez, J.M., Schuverdt, M.L.: Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111, 5-32 (2008)
    • (2008) Math. Program. , vol.111 , pp. 5-32
    • Andreani, R.1    Birgin, E.G.2    Martínez, J.M.3    Schuverdt, M.L.4
  • 3
    • 0001531895 scopus 로고
    • Two point step size gradient method
    • Barzilai, J., Borwein, J.M.: Two point step size gradient method. 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
  • 4
    • 0000377218 scopus 로고
    • Projected Newton methods for optimization problems with simple constrains
    • Bertsekas, D.P.: Projected Newton methods for optimization problems with simple constrains. SIAM J. Control. Optim. 20, 221-246 (1982)
    • (1982) SIAM J. Control. Optim. , vol.20 , pp. 221-246
    • 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.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 22, 101-125 (2002)
    • (2002) Comput. Optim. Appl. , vol.22 , 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.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196-1121 (2000)
    • (2000) SIAM J. Optim. , vol.10 , pp. 1196-1121
    • 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.: Algorithm 813: SPG-software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340-349 (2001)
    • (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.: Inexact spectral projected gradient methods on convex sets. IMA J. Numer. Anal. 23, 539-559 (2003)
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 539-559
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 9
    • 1642543147 scopus 로고    scopus 로고
    • A limited memory multipoint secant method for bound constrained optimization
    • Burdakov, O.P., Martínez, J.M., Pilotta, E.A.: A limited memory multipoint secant method for bound constrained optimization. Annal. Oper. Res. 117, 51-70 (2002)
    • (2002) Annal. Oper. Res. , vol.117 , pp. 51-70
    • Burdakov, O.P.1    Martínez, J.M.2    Pilotta, E.A.3
  • 10
    • 0000732463 scopus 로고
    • A limited memory algorithm for bound constrained optimization
    • Byrd, R.H., Lu, P.H., Nocedal, J.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Stat. Comput. 16, 1190-1208 (1995)
    • (1995) SIAM J. Sci. Stat. Comput. , vol.16 , pp. 1190-1208
    • Byrd, R.H.1    Lu, P.H.2    Nocedal, J.3
  • 11
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithm for optimization with simple bounds
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Global convergence of a class of trust region algorithm for optimization with simple bounds. SIAM J. Numer. Anal. 25, 433-460 (1988)
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 12
    • 0026136104 scopus 로고
    • A globally convergent augmented Lagrangean algorithm for optimization with general constraints and simple bounds
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L.: A globally convergent augmented Lagrangean algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28, 545-572 (1991)
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 545-572
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 13
    • 0000024679 scopus 로고
    • CUTE: Constrained and unconstrained testing environment
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L.: CUTE: constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123-160 (1995)
    • (1995) ACM Trans. Math. Softw. , vol.21 , pp. 123-160
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 14
    • 15544385032 scopus 로고    scopus 로고
    • Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
    • 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
  • 15
    • 21644488546 scopus 로고    scopus 로고
    • On the asymptotic behaviour of some new gradient methods
    • Dai, Y.H., Fletcher, R.: On the asymptotic behaviour of some new gradient methods. Math. Program. (Ser. A) 13, 541-559 (2005)
    • (2005) Math. Program. (Ser. A) , vol.13 , pp. 541-559
    • Dai, Y.H.1    Fletcher, R.2
  • 16
    • 0036102376 scopus 로고    scopus 로고
    • R-linear convergence of the Barzilai and Borwein gradient method
    • Dai, Y.H., Liao, L.Z.: R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 26, 1-10 (2006)
    • (2006) IMA J. Numer. Anal. , vol.26 , pp. 1-10
    • Dai, Y.H.1    Liao, L.Z.2
  • 17
    • 0036539289 scopus 로고    scopus 로고
    • Modified two-point stepsize gradient methods for unconstrained optimization
    • Dai, Y.H., Yuan, J.Y., Yuan, Y.: Modified two-point stepsize gradient methods for unconstrained optimization. Comput. Optim. Appl. 22, 103-109 (2002)
    • (2002) Comput. Optim. Appl. , vol.22 , pp. 103-109
    • Dai, Y.H.1    Yuan, J.Y.2    Yuan, Y.3
  • 18
    • 33745923778 scopus 로고    scopus 로고
    • The cyclic Barzilai-Borwein method for unconstrained optimization
    • Dai, Y.H., Hager, W.W., Schittkowski, K., Zhang, H.: The cyclic Barzilai-Borwein method for unconstrained optimization. IMA J. Numer. Anal. 26, 604-627 (2006)
    • (2006) IMA J. Numer. Anal. , vol.26 , pp. 604-627
    • Dai, Y.H.1    Hager, W.W.2    Schittkowski, K.3    Zhang, H.4
  • 19
    • 8644224162 scopus 로고    scopus 로고
    • Augmented Lagrangian algorithm based on the spectral projected gradient for solving nonlinear programming problems
    • Diniz-Ehrhardt, M.A., Gomes-Ruggiero, M.A., Martínez, J.M., Santos, S.A.: Augmented Lagrangian algorithm based on the spectral projected gradient for solving nonlinear programming problems. J. Optim. Theory Appl. 123, 497-517 (2004)
    • (2004) J. Optim. Theory Appl. , vol.123 , pp. 497-517
    • Diniz-Ehrhardt, M.A.1    Gomes-Ruggiero, M.A.2    Martínez, J.M.3    Santos, S.A.4
  • 20
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201-213 (2002)
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.D.1    Moré, J.J.2
  • 21
    • 0038342659 scopus 로고    scopus 로고
    • An active set Newton's algorithm for large-scale nonlinear programs with box constraints
    • Facchinei, F., Júdice, J., Soares, J.: An active set Newton's algorithm for large-scale nonlinear programs with box constraints. SIAM J. Optim. 8, 158-186 (1998)
    • (1998) SIAM J. Optim. , vol.8 , pp. 158-186
    • Facchinei, F.1    Júdice, J.2    Soares, J.3
  • 22
    • 0036433456 scopus 로고    scopus 로고
    • A truncated Newton algorithm for large scale box constrained optimization
    • Facchinei, F., Lucidi, S., Palagi, L.: A truncated Newton algorithm for large scale box constrained optimization. SIAM J. Optim. 12, 1100-1125 (2002)
    • (2002) SIAM J. Optim. , vol.12 , pp. 1100-1125
    • Facchinei, F.1    Lucidi, S.2    Palagi, L.3
  • 23
    • 0036853835 scopus 로고    scopus 로고
    • Nonmonotone globalization techniques for the Barzilai-Borwein gradient method
    • Grippo, L., Sciandrone, M.: Nonmonotone globalization techniques for the Barzilai-Borwein gradient method. Comput. Optim. Appl. 23, 143-169 (2002)
    • (2002) Comput. Optim. Appl. , vol.23 , pp. 143-169
    • Grippo, L.1    Sciandrone, M.2
  • 24
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • 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
  • 25
    • 0014538507 scopus 로고
    • Extension of Davidon's variable metric algorithm to maximization under linear inequality and constraints
    • Goldfarb, D.: Extension of Davidon's variable metric algorithm to maximization under linear inequality and constraints. SIAM J. Appl. Math. 17, 739-764 (1969)
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 739-764
    • Goldfarb, D.1
  • 26
    • 19844363263 scopus 로고    scopus 로고
    • Toint, Numerical methods for large-scale nonlinear optimization
    • Gould, N.I.M., Orban, D., L, Ph.: Toint, Numerical methods for large-scale nonlinear optimization. Acta Numer. 14, 299-361 (2005)
    • (2005) Acta Numer. , vol.14 , pp. 299-361
    • Gould, N.I.M.1    Orban, D.2    Ph., L.3
  • 27
    • 34249008073 scopus 로고    scopus 로고
    • A new active set algorithm for box constrained optimization
    • Hager, W.W., Zhang, H.: A new active set algorithm for box constrained optimization. SIAM J. Optim. 17, 526-557 (2006)
    • (2006) SIAM J. Optim. , vol.17 , pp. 526-557
    • Hager, W.W.1    Zhang, H.2
  • 28
    • 0342572634 scopus 로고    scopus 로고
    • Validation of an augmented Lagrangian algorithm with a Gauss-Newton Hessian approximation using a set of hard-spheres problems
    • Krejić, N., Martínez, J.M., Mello, M.P., Pilotta, E.A.: Validation of an augmented Lagrangian algorithm with a Gauss-Newton Hessian approximation using a set of hard-spheres problems. Comput. Optim. Appl. 16, 247-263 (2000)
    • (2000) Comput. Optim. Appl. , vol.16 , pp. 247-263
    • Krejić, N.1    Martínez, J.M.2    Mello, M.P.3    Pilotta, E.A.4
  • 30
    • 0002579671 scopus 로고    scopus 로고
    • BOX-QUACAN and the implementation of Augmented Lagrangian algorithms for minimization with inequality constraints
    • Martínez, J.M.: BOX-QUACAN and the implementation of Augmented Lagrangian algorithms for minimization with inequality constraints. Comput. Appl. Math. 19, 31-56 (2000)
    • (2000) Comput. Appl. Math. , vol.19 , pp. 31-56
    • Martínez, J.M.1
  • 31
    • 0031525729 scopus 로고    scopus 로고
    • A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization
    • Ni, Q., Yuan, Y.: A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization. Math. Comput. 66, 1509-1520 (1997)
    • (1997) Math. Comput. , vol.66 , pp. 1509-1520
    • Ni, Q.1    Yuan, Y.2
  • 32
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • Raydan, M.: On the Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. IMA J. Numer. Anal. 13, 321-326 (1993)
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 33
    • 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. Optim. 7, 26-33 (1997)
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 34
    • 9944262108 scopus 로고    scopus 로고
    • A nonmonotone line search technique and its application to unconstrained optimization
    • Zhang, H., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043-1056 (2004)
    • (2004) SIAM J. Optim. , vol.14 , pp. 1043-1056
    • Zhang, H.1    Hager, W.W.2


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