163
Views
21
CrossRef citations to date
0
Altmetric
The International Conference on Engineering Optimization (EngOpt 2008)

Limited memory bundle method for large bound constrained nonsmooth optimization: convergence analysis

&
Pages 895-916 | Received 07 Oct 2008, Accepted 23 Feb 2009, Published online: 23 Mar 2009

References

  • Ben-Tal , A. and Nemirovski , A. 2005 . Non-Euclidean restricted memory level method for large-scale convex optimization . Math. Program , 102 ( 3 ) : 407 – 456 .
  • Bihain , A. 1984 . Optimization of upper semidifferentiable functions . J. Optim. Theory Appl. , 4 : 545 – 568 .
  • Byrd , R. H. , Lu , P. , Nocedal , J. and Zhu , C. 1995 . A limited memory algorithm for bound constrained optimization . SIAM J. Sci. Comput. , 16 ( 5 ) : 1190 – 1208 .
  • Byrd , R. H. , Nocedal , J. and Schnabel , R. B. 1994 . Representations of quasi-Newton matrices and their use in limited memory methods . Math. Program , 63 : 129 – 156 .
  • Clarke , F. H. 1983 . Optimization and Nonsmooth Analysis , New York : Wiley-Interscience .
  • Clarke , F. H. , Ledyaev , Y. S. , Stern , R. J. and Wolenski , P. R. 1998 . Nonsmooth Analysis and Control Theory , New York : Springer .
  • Conn , A. R. , Gould , N. I.M. and Toint , P. L. 1988 . Global convergence of a class of trust region algorithms for optimization with simple bounds . SIAM J. Numer. Anal. , 25 ( 2 ) : 433 – 460 .
  • Conn , A. R. , Gould , N. I.M. and Toint , P. L. 1988 . Testing a class of methods for solving minimization problems with simple bounds on the variables . Math. Comput. , 50 ( 182 ) : 399 – 430 .
  • Dolan , E. D. and Moré , J. J. 2002 . Benchmarking optimization software with performance profiles . Math. Program , 91 : 201 – 213 .
  • Fletcher , R. 1987 . Practical Methods of Optimization , 2 , Chichester : John Wiley and Sons .
  • Gilbert , J.-C. and Lemaréchal , C. 1989 . Some numerical experiments with variable-storage quasi-Newton algorithms . Math. Program , 45 : 407 – 435 .
  • Haarala , M. 2004 . Large-scale nonsmooth optimization: Variable metric bundle method with limited memory , Department of Mathematical Information Technology, University of Jyväskylä . Ph.D. thesis
  • Haarala , M. , Miettinen , K. and Mäkelä , M. M. 2004 . New limited memory bundle method for large-scale nonsmooth optimization . Optim. Methods Softw. , 19 ( 6 ) : 673 – 692 .
  • Haarala , N. , Miettinen , K. and Mäkelä , M. M. 2007 . Globally convergent limited memory bundle method for large-scale nonsmooth optimization . Math. Program , 109 ( 1 ) : 181 – 205 .
  • Hiriart-Urruty , J.-B. and Lemaréchal , C. 1993 . Convex Analysis and Minimization Algorithms I , Berlin : Springer-Verlag .
  • Hiriart-Urruty , J.-B. and Lemaréchal , C. 1993 . Convex Analysis and Minimization Algorithms II , Berlin : Springer-Verlag .
  • Kärkkäinen , T. , Majava , K. and Mäkelä , M. M. 2001 . Comparison of formulations and solution methods for image restoration problems . Inverse Problems , 17 ( 6 ) : 1977 – 1995 .
  • Karmitsa , N. and Mäkelä , M. M. 2008 . Globally convergent limited memory bundle algorithm for nondifferentiable programming subject to box constraints , Turku : Turku Centre for Computer Science . TUCS Tech. Rep. No. 882
  • Karmitsa , N. and Mäkelä , M. M. Adaptive limited memory bundle method for bound constrained large-scale nonsmooth optimization . Optimization , (to appear)
  • Kiwiel , K. C. 1985 . Methods of Descent for Nondifferentiable Optimization , Vol. 1133 , Berlin : Springer-Verlag . Lecture Notes in Mathematics
  • Lemaréchal , C. , Strodiot , J.-J. and Bihain , A. 1981 . “ On a bundle algorithm for nonsmooth optimization ” . In Nonlinear Programming , Edited by: Mangasarian , O. L. , Mayer , R. R. and Robinson , S. M. 285 – 281 . New York : Academic Press .
  • Liu , D. C. and Nocedal , J. 1989 . On the limited memory BFGS method for large scale optimization . Math. Program , 45 : 503 – 528 .
  • Lukšan , L. and Vlcšek , J. 1999 . Globally convergent variable metric method for convex nonsmooth unconstrained minimization . J. Optim. Theory Appl. , 102 ( 3 ) : 593 – 613 .
  • Mäkelä , M. M. 2002 . Survey of bundle methods for nonsmooth optimization . Optim. Methods Softw. , 17 ( 1 ) : 1 – 29 .
  • Mäkelä , M. M. 2003 . Multiobjective proximal bundle method for nonconvex nonsmooth optimization: Fortran subroutine MPBNGC 2.0 , Reports of the Department of Mathematical Information Technology Series B, Scientific Computing B. 13/2003 Jyväskylä : University of Jyväskylä .
  • Mäkelä , M. M. and Neittaanmäki , P. 1992 . Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control , Singapore : World Scientific Publishing Co .
  • Mifflin , R. 1982 . A modification and an extension of Lemaréchal's algorithm for nonsmooth minimization . Math. Program. Study , 17 : 77 – 90 .
  • Mistakidis , E. S. and Stavroulakis , G. E. 1998 . Nonconvex Optimization in Mechanics: Smooth and Nonsmooth Algorithms, Heuristics and Engineering Applications by the F.E.M , Dordrecht : Kluwer Academic Publishers .
  • Moreau , J. J. , Panagiotopoulos , P. D. and Strang , G. 1988 . Topics in Nonsmooth Mechanics , Edited by: Moreau , J. J. , Panagiotopoulos , P. D. and Strang , G. Basel : Birkhäuser Verlag .
  • Nocedal , J. 1980 . Updating quasi-Newton matrices with limited storage . Math. Comput. , 35 ( 151 ) : 773 – 782 .
  • Outrata , J. , Kočvara , M. and Zowe , J. 1998 . Nonsmooth Approach to Optimization Problems With Equilibrium Constraints: Theory, Applications and Numerical Results , Dordrecht : Kluwer Academic Publisher .
  • Panier , E. R. 1987 . An active set method for solving linearly constrained nonsmooth optimization problems . Math. Program , 37 : 269 – 292 .
  • Schramm , H. and Zowe , J. 1992 . A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results . SIAM J. Optim. , 2 ( 1 ) : 121 – 152 .
  • Vlček , J. and Lukšan , L. 2001 . Globally convergent variable metric method for nonconvex nondifferentiable unconstrained minimization . J. Optim. Theory Appl. , 111 ( 2 ) : 407 – 430 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.