36
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Sensitivity analysis of nondifferentiable sums of singular values of rectangular matrices

Pages 247-260 | Published online: 02 Nov 2010

References

  • Bhatia . 1987 . “ Perturbation bounds for the matrix eigenvalues ” . In Research Notes in Mathematics , Vol. 162 , Pitman Publishers .
  • Chenais and Rousselet , B. 1990 . Continuité et différentiabilité d'éléments propres :application á l' optimisation de structures . Appl. Math. Optim. , 22 : 27 – 59 .
  • Chenais , D. and Rousselet , B. 1990 . Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve . Math. Mod. and Num. Anal. , 24 : 307 – 341 .
  • Clarke , F. H. 1983 . Optimization and nonsmooth analysis , New York : Wiley-Interscience Publication .
  • Correa , R. and Seeger , A. 1985 . Directional derivative of a minimax function . Nonlinear Anal. T.M.A. , 9 : 13 – 22 .
  • Cullum , J. , Donath , W. E. and .Wolfe , P. 1985 . The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices . Math.Programming Study , 3
  • Danskin , J. M. 1967 . The theory of max-min and its applications to weapons allocations problems , New York : Springer-Verlag .
  • Fletcher , R. 1985 . Semi–definite matrix constraints in optimization . SIAM J. Control and Opt. , 23 : 493 – 513 .
  • Gollan , B. 1987 . Eigenvalue perturbations and nonlinear parametric optimization . Math.Programming Study , 30 : 67 – 81 .
  • Hiriart–Urruty , J. B. 1979 . New concepts in nondifferentiable programming . Bull. Soc. Math. France, Memoire , 60 : 57 – 85 .
  • Hiriart–Urruty , J. B. 1982 . “ ε–subdifferential calculus ” . In In Research Notes in Mathematics , Vol. 57 , 43 – 92 . Pitman Publishers .
  • Hiriart–Urruty , J. B. 1989 . “ From convex optimization to nonconvex optimization ” . In Part I, In Nonsmooth Optimization and Related Topics , Edited by: Clarke , F. H. , Demyanov , V. F. and Giannessi , E. 219 – 239 . Plenum Press .
  • Hiriart–Urruty , J. B. , Seeger , A. and Ye , D. 1992 . “ Sensitivity analysis for a class of convex functions defined on a space of matrices ” . In In Advances in Optimization, Lect. Notes in Economics and Mathematical Systems , Edited by: Oettli , W. and Pallaschke , D. Vol. 382 , 133 – 154 . Springer-Verlag .
  • Horn , R. and Johnson , C. 1985 . Matrix Analysis , Cambridge Univ. Press .
  • Marshall , A. and Olkin , I. 1979 . “ Inequalities :Theory of majorization and its applications ” . In Mathematics in Science and Engineering , Vol. 143 , Academic Press Inc. .
  • Overton , M. 1988 . On minimizing the maximum eigenvalue of a symmetric matrix . SIAM J. Matrix Anal. Appl. , 9 : 256 – 268 .
  • Overton , M. L. and Womersley , R. S. 1988 . On minimizing the spectral radius of a nonsymmetric matrix function :optimality and duality theory . SIAM J. Matrix Anal. Appl. , 9 : 473 – 498 .
  • Overton , M. L. and Womersley , R. S. June 1991 . Optimality conditions and duality theory for minimizing sums of the largests eigenvalues of symmetric matrices June , Preprint
  • Overton , M. L. and Womersley , R. S. 1992 . On the sum of the largest eigenvalues of a symmetric matrix . SIAM J. Matrix Anal. Appl. , 13 June : 41 – 45 .
  • Pchenitchny , B. W. 1971 . Necessary conditions for an extremum , New York : Dekker .
  • Polak and Wardi , Y. 1982 . Nondifferentiable optimization algorithm for designing control systems having singular value inequalities. Automatica . 18
  • Rockafellar , R. T. 1970 . Convex Analysis , Princeton, N.J. : Princeton Univ. Press .
  • Rockafellar , R. T. 1979 . La théorie des sous–gradients et ses applications á l'optimization :fonctions convexes et non convexes , De Montréal : Presses de l'Univ. .
  • Rockafellar , R. T. 1982 . “ Favorable classes of Lipschitz continuous functions in subgradient optimization ” . In Nondifferentiable Optimization , Edited by: Nurminski , E. 125 – 143 . New York : Pergamon Press .
  • Spingarn , J. E. 1981 . Submonotone subdifferentials of Lipschitz functions . Trans. Am. Math. Soc. , 264 : 77 – 89 .
  • Ye , D. 1990 . “ Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ε-subdifferential of the associated convex quadratic form ” . Toulouse : Lab. d'Analyse Numérique, Univ. Paul Sabatier . Preprint

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.