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Volumn 109, Issue 1, 2007, Pages 181-205

Globally convergent limited memory bundle method for large-scale nonsmooth optimization

Author keywords

Bundle methods; Global convergence; Large scale optimization; Limited memory methods; Nondifferentiable programming; Variable metric methods

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; OPTIMIZATION;

EID: 33845348915     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0728-2     Document Type: Article
Times cited : (95)

References (34)
  • 1
    • 0035546519 scopus 로고    scopus 로고
    • Bundle methods in stochastic optimal power management: A disaggregated approach using preconditioners
    • Bacaud, L., Lemaréchal, C., Renaud, A., Sagastizábal, C.: Bundle methods in stochastic optimal power management: A disaggregated approach using preconditioners. Comput. Optim. Appl. 20 (3), 227-244 (2001)
    • (2001) Comput. Optim. Appl. , vol.20 , Issue.3 , pp. 227-244
    • Bacaud, L.1    Lemaréchal, C.2    Renaud, A.3    Sagastizábal, C.4
  • 2
    • 0021620494 scopus 로고
    • Optimization of upper semidifferentiable functions
    • Bihain, A.: Optimization of upper semidifferentiable functions. J. Optimization Theory Appl. 4, 545-568 (1984)
    • (1984) J. Optimization Theory Appl. , vol.4 , pp. 545-568
    • Bihain, A.1
  • 3
    • 0028319529 scopus 로고
    • Representations of quasi-Newton matrices and their use in limited memory methods
    • Byrd, R.H., Nocedal, J., Schnabel, R.B.: Representations of quasi-Newton matrices and their use in limited memory methods. Math. Program. 63, 129-156 (1994)
    • (1994) Math. Program. , vol.63 , pp. 129-156
    • Byrd, R.H.1    Nocedal, J.2    Schnabel, R.B.3
  • 6
    • 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
  • 8
    • 34249975203 scopus 로고
    • Some numerical experiments with variable-storage quasi-Newton algorithms
    • Gilbert, J.C., Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms. Math. Program. 45, 407-435 (1989)
    • (1989) Math. Program. , vol.45 , pp. 407-435
    • Gilbert, J.C.1    Lemaréchal, C.2
  • 9
    • 0013203809 scopus 로고    scopus 로고
    • Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation
    • C. Greengard, A. Ruszczynski (eds.) Decision Making under Uncertainty: Energy and Power, Springer, New York
    • Gröwe-Kuska, N., Kiwiel, K.C., Nowak, M.P., Römisch, W., Wegner, I.: Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation. In: C. Greengard, A. Ruszczynski (eds.) Decision Making under Uncertainty: Energy and Power, IMA Volumes in Mathematics and its Applications, vol. 128, Springer, New York, 2002, pp. 39-70
    • (2002) IMA Volumes in Mathematics and Its Applications , vol.128 , pp. 39-70
    • Gröwe-Kuska, N.1    Kiwiel, K.C.2    Nowak, M.P.3    Römisch, W.4    Wegner, I.5
  • 11
    • 9944244537 scopus 로고    scopus 로고
    • New limited memory bundle method for large-scale nonsmooth optimization
    • Haarala, M., Miettinen, K., Mäkelä, M.M.: New limited memory bundle method for large-scale nonsmooth optimization. Optim. Methods Softw. 19 (6), 673-692 (2004)
    • (2004) Optim. Methods Softw. , vol.19 , Issue.6 , pp. 673-692
    • Haarala, M.1    Miettinen, K.2    Mäkelä, M.M.3
  • 14
    • 0035661920 scopus 로고    scopus 로고
    • Comparison of formulations and solution methods for image restoration problems
    • Kärkkäinen, T., Majava, K., Mäkelä, M.M.: Comparison of formulations and solution methods for image restoration problems. Inverse Probl. 17 (6), 1977-1995 (2001)
    • (2001) Inverse Probl. , vol.17 , Issue.6 , pp. 1977-1995
    • Kärkkäinen, T.1    Majava, K.2    Mäkelä, M.M.3
  • 15
    • 0003296464 scopus 로고
    • Methods of descent for nondifferentiable optimization
    • Springer-Verlag, Berlin
    • Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics 1133. Springer-Verlag, Berlin, 1985
    • (1985) Lecture Notes in Mathematics , vol.1133
    • Kiwiel, K.C.1
  • 16
    • 0001260166 scopus 로고
    • A method for solving certain quadratic programming problems arising in nonsmooth optimization
    • Kiwiel, K.C.: A method for solving certain quadratic programming problems arising in nonsmooth optimization. IMA J. Numer. Anal. 6, 137-152 (1986)
    • (1986) IMA J. Numer. Anal. , vol.6 , pp. 137-152
    • Kiwiel, K.C.1
  • 17
    • 77957820648 scopus 로고
    • Nondifferentiable optimization
    • G.L. Nemhauser, A.H.G. Rinnooy Kan, M.J. Todd (eds.) Elsevier North-Holland, Inc., New York
    • Lemaréchal, C.: Nondifferentiable optimization. In: G.L. Nemhauser, A.H.G. Rinnooy Kan, M.J. Todd (eds.) Optimization. Elsevier North-Holland, Inc., New York, 1989, pp. 529-572
    • (1989) Optimization , pp. 529-572
    • Lemaréchal, C.1
  • 18
    • 0000851851 scopus 로고
    • On a bundle algorithm for nonsmooth optimization
    • O.L. Mangasarian, R.R. Mayer, S.M. Robinson (eds.) Academic Press, New York
    • Lemaréchal, C., Strodiot, J.J., Bihain, A.: On a bundle algorithm for nonsmooth optimization. In: O.L. Mangasarian, R.R. Mayer, S.M. Robinson (eds.) Nonlinear Programming. Academic Press, New York, 1981, pp. 285-281
    • (1981) Nonlinear Programming , pp. 285-1281
    • Lemaréchal, C.1    Strodiot, J.J.2    Bihain, A.3
  • 19
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization
    • Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Program. 45, 503-528 (1989)
    • (1989) Math. Program. , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 20
    • 0033245906 scopus 로고    scopus 로고
    • Globally convergent variable metric method for convex nonsmooth unconstrained minimization
    • Lukšan, L., Vlček, J.: Globally convergent variable metric method for convex nonsmooth unconstrained minimization. J. Optimization Theory Appl. 102, 593-613 (1999)
    • (1999) J. Optimization Theory Appl. , vol.102 , pp. 593-613
    • Lukšan, L.1    Vlček, J.2
  • 22
    • 0036462808 scopus 로고    scopus 로고
    • Survey of bundle methods for nonsmooth optimization
    • Mäkelä, M.M.: Survey of bundle methods for nonsmooth optimization. Optim. Methods Softw. 17 (1), 1-29 (2002)
    • (2002) Optim. Methods Softw. , vol.17 , Issue.1 , pp. 1-29
    • Mäkelä, M.M.1
  • 23
    • 0001525323 scopus 로고    scopus 로고
    • Comparing nonsmooth nonconvex bundle methods in solving hemivariational inequalities
    • Mäkelä, M.M., Miettinen, M., Lukšan, L., Vlček, J.: Comparing nonsmooth nonconvex bundle methods in solving hemivariational inequalities. J. Glob. Optim. 14, 117-135 (1999)
    • (1999) J. Glob. Optim. , vol.14 , pp. 117-135
    • Mäkelä, M.M.1    Miettinen, M.2    Lukšan, L.3    Vlček, J.4
  • 25
    • 0003108675 scopus 로고
    • A modification and an extension of Lemaráchal's algorithm for nonsmooth minimization
    • Mifflin, R.: A modification and an extension of Lemaráchal's algorithm for nonsmooth minimization. Math. Program. Study 17, 77-90 (1982)
    • (1982) Math. Program. Study , vol.17 , pp. 77-90
    • Mifflin, R.1
  • 27
    • 0003777056 scopus 로고
    • Moreau, J.J., Panagiotopoulos, P.D., Strang, G. (eds.): Birkhäuser Verlag, Basel
    • Moreau, J.J., Panagiotopoulos, P.D., Strang, G. (eds.): Topics in Nonsmooth Mechanics. Birkhäuser Verlag, Basel, 1988
    • (1988) Topics in Nonsmooth Mechanics
  • 29
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • Nocedal, J.: Updating quasi-Newton matrices with limited storage. Math. Comput. 35 (151), 773-782 (1980)
    • (1980) Math. Comput. , vol.35 , Issue.151 , pp. 773-782
    • Nocedal, J.1
  • 30
    • 33845307155 scopus 로고    scopus 로고
    • Stochastic programming for power production and trading under uncertainty
    • W. Jäger, H.J. Krebs (eds.) Springer, Berlin
    • Nowak, M.P., Nürnberg, R., Römisch, W., Schultz, R., Westphalen, M.: Stochastic programming for power production and trading under uncertainty. In: W. Jäger, H.J. Krebs (eds.) Mathematics - Key Technology for the Future. Springer, Berlin, 2003, pp. 623-636
    • (2003) Mathematics - Key Technology for the Future , pp. 623-636
    • Nowak, M.P.1    Nürnberg, R.2    Römisch, W.3    Schultz, R.4    Westphalen, M.5
  • 31
    • 0003534283 scopus 로고    scopus 로고
    • Nonsmooth approach to optimization problems with equilibrium constraints
    • Kluwert Academic Publisher, Dordrecht
    • Outrata, J., Kočvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems With Equilibrium Constraints. Theory, Applications and Numerical Results. Kluwert Academic Publisher, Dordrecht, 1998
    • (1998) Theory, Applications and Numerical Results
    • Outrata, J.1    Kočvara, M.2    Zowe, J.3
  • 33
    • 0000091855 scopus 로고
    • A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results
    • Schramm, H., Zowe, J.: A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results. SIAM J. Optim. 2 (1), 121-152 (1992)
    • (1992) SIAM J. Optim. , vol.2 , Issue.1 , pp. 121-152
    • Schramm, H.1    Zowe, J.2
  • 34
    • 0040780606 scopus 로고    scopus 로고
    • Globally convergent variable metric method for nonconvex nondifferentiable unconstrained minimization
    • Vlček, J., Lukšan, L.: Globally convergent variable metric method for nonconvex nondifferentiable unconstrained minimization. J. Optimization Theory Appl. 111 (2), 407-430 (2001)
    • (2001) J. Optimization Theory Appl. , vol.111 , Issue.2 , pp. 407-430
    • Vlček, J.1    Lukšan, L.2


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