A unified optimality condition for eigenvalue problems

Wen Bin Liu; Julio E. Rubio

Kybernetika (1993)

  • Volume: 29, Issue: 3, page 249-255
  • ISSN: 0023-5954

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Liu, Wen Bin, and Rubio, Julio E.. "A unified optimality condition for eigenvalue problems." Kybernetika 29.3 (1993): 249-255. <http://eudml.org/doc/28260>.

@article{Liu1993,
author = {Liu, Wen Bin, Rubio, Julio E.},
journal = {Kybernetika},
keywords = {abstract elliptic differential operator; Hilbert space; optimal design; nonsmooth optimization},
language = {eng},
number = {3},
pages = {249-255},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A unified optimality condition for eigenvalue problems},
url = {http://eudml.org/doc/28260},
volume = {29},
year = {1993},
}

TY - JOUR
AU - Liu, Wen Bin
AU - Rubio, Julio E.
TI - A unified optimality condition for eigenvalue problems
JO - Kybernetika
PY - 1993
PB - Institute of Information Theory and Automation AS CR
VL - 29
IS - 3
SP - 249
EP - 255
LA - eng
KW - abstract elliptic differential operator; Hilbert space; optimal design; nonsmooth optimization
UR - http://eudml.org/doc/28260
ER -

References

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  2. A. S. Bratus, Condition of extremum for eigenvalues of some elliptic boundary value problems, J. Optim. Theory Appl. 68 (1991), 423-437. (1991) MR1097311
  3. F. Clarke, Optimization and Nonsmooth Analysis, J. Wiley, New York 1983. (1983) Zbl0582.49001MR0709590
  4. K. Choi, E. J. Haug, Optimization of structures with repeated eigenvalues, In: Optimal Design of Distributed Structures (E. J. Haug and J. Cea, eds.), Sijthoff-Noordhoff, Leyden 1981, pp. 219-277. (1981) Zbl0543.73117MR0690966
  5. S. J. Cox, M. L. Overton, On the optimal design of columns against buckling, Preprint of Rice university 1990, TR90-13. (1990) MR1147865
  6. M. Delfour, J. P. Zolesio, Shape sensitivity analysis via min max differentiability, SIAM J. Control Optim. 26 (1988), 835-863. (1988) Zbl0654.49010MR0948649
  7. Z. Z. Guang, G. C. Zhang, Linear Functional Analysis, Science Press of Shangai, Shanghai 1979 (in Chinese). (1979) 
  8. E. J. Haug, B. Rousselet, Design sensitivity of eigenvalue variations, In: Optimal Design of Distributed Structures (E. J. Haug and J. Cea, eds.), Sijthoff-Noordhoff, Leyden 1981, pp. 1370-1396. (1981) 
  9. A. D. loffe, Necessary and sufficient conditions for a local minimum I, SIAM J. Control Optim. 17 (1979), 245-250. (1979) MR0525025
  10. F. Lempio, H. Maurer, Differential stability in infinite-dimensional nonlinear programming, Appl. Math. Optim. 6 (1980), 139-152. (1980) Zbl0426.90072MR0563531
  11. E. Masur, Optimal structural design under multiple eigenvalue constraints, Internat. J. Solids and Structures 20 (1984), 211-231. (1984) Zbl0544.73117MR0735699
  12. N. Olhoff, S. Rasmussen, On single and bimodal optimum buckling loads of clamped columns, Internat. J. Solids and Structures 75 (1977), 605-614. (1977) Zbl0357.73041
  13. I. Tadjbakhsh, J. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, J. Appl. Mech. 29 (1962), 159-164. (1962) Zbl0106.38301MR0137381
  14. J. P. Zalesio, Semi-derivatives of repeated eigenvalues, In: Optimal Design of Distributed Structures (E.J. Haug and J. Cea, eds.), Sijthoff-Noordhoff, Leyden 1981, pp. 1457-1473. (1981) 

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