Free Access
Volume 22, Number 1, January-March 2016
Page(s) 64 - 87
Published online 02 September 2015
  1. G. Allaire, Conception optimale de structures, Vol. 58 of Mathématiques & Applications (Berlin)[Mathematics & Applications]. With the collaboration of Marc Schoenauer (INRIA) in the writing of Chapter 8. Springer-Verlag, Berlin (2007). [Google Scholar]
  2. G. Allaire and C. Dapogny, A linearized approach to worst-case design in parametric and geometric shape optimization. Math. Models Methods Appl. Sci. 24 (2014) 2199–2257. [CrossRef] [Google Scholar]
  3. G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (2004) 363–393. [CrossRef] [Google Scholar]
  4. S. Amstutz, Sensitivity analysis with respect to a local perturbation of the material property. Asymptot. Anal. 49 (2006) 87–108. [MathSciNet] [Google Scholar]
  5. S. Amstutz, Analysis of a level set method for topology optimization. Optim. Methods Softw. 26 (2011) 555–573. [Google Scholar]
  6. S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method. J. Comput. Phys. 216 (2006) 573–588. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Amstutz and M. Ciligot-Travain, Optimality conditions for shape and topology optimization subject to a cone constraint. SIAM J. Control Optim. 48 (2010) 4056–4077. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. Babuška, F. Nobile and R. Tempone, Worst case scenario analysis for elliptic problems with uncertainty. Numer. Math. 101 (2005) 185–219. [CrossRef] [MathSciNet] [Google Scholar]
  9. Y. Ben-Haim, Information-gap Decision Theory. Series on Decision and Risk. Academic Press Inc., San Diego, CA (2001). Decisions under severe uncertainty. [Google Scholar]
  10. A. Ben-Tal, L. El Ghaoui and A. Nemirovski, Robust optimization. Princeton Series Appl. Math. Princeton University Press, Princeton, NJ (2009). [Google Scholar]
  11. M.P. Bendsøe and O. Sigmund, Topology optimization. Theory, Methods and Appl. Springer-Verlag, Berlin (2003). [Google Scholar]
  12. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer Ser. Oper. Res. Springer-Verlag, New York (2000). [Google Scholar]
  13. A. Cherkaev and E. Cherkaev, Optimal design for uncertain loading condition. In Homogenization. Vol. 50 of Ser. Adv. Math. Appl. Sci.. World Sci. Publ., River Edge, NJ (1999) 193–213. [Google Scholar]
  14. E. Cherkaev and A. Cherkaev, Principal compliance and robust optimal design. Essays and papers dedicated to the memory of Clifford Ambrose Truesdell III. Vol. III. J. Elasticity 72 (2003) 71–98 [CrossRef] [MathSciNet] [Google Scholar]
  15. F. de Gournay, G. Allaire and F. Jouve, Shape and topology optimization of the robust compliance via the level set method. ESAIM Control Optim. Calc. Var. 14 (2008) 43–70. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  16. J.-M. Feng, G.-X. Lin, R.-L. Sheu and Y. Xia, Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint. J. Global Optim. 54 (2012) 275–293. [CrossRef] [MathSciNet] [Google Scholar]
  17. O. Flippo and B. Jansen, Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid. Eur. J. Oper. Res. 94 (1996) 167–178. [CrossRef] [Google Scholar]
  18. C. Fortin and H. Wolkowicz, The trust region subproblem and semidefinite programming. Optim. Methods Softw. 19 (2004) 41–67. [CrossRef] [Google Scholar]
  19. A.L. Fradkov and V.A. Jakubovič, The S-procedure and the duality relation in convex quadratic programming problems. Vestnik Leningrad. Univ. (1 Mat. Meh. Astronom. Vyp. 1) 155 (1973) 81–87. [Google Scholar]
  20. A.L. Fradkov and V.A. Jakubovič, The S-procedure and the duality relation in convex quadratic programming problems. Vestnik Leningrad. Univ. 6 (1979) 101–109. [Google Scholar]
  21. S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756–1778. [Google Scholar]
  22. D.M. Gay, Computing optimal locally constrained steps. SIAM J. Sci. Statis. Comput. 2 (1981) 186–197. [CrossRef] [MathSciNet] [Google Scholar]
  23. X. Guo, W. Zhang and L. Zhang, Robust structural topology optimization considering boundary uncertainties. Comput. Methods Appl. Mech. Engrg. 253 (2013) 356–368. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Hinrichsen and A.J. Pritchard, Real and complex stability radii: a survey. In Control of uncertain systems (Bremen, 1989). Vol. 6 of Progr. Systems Control Theory. Birkhäuser Boston, Boston, MA (1990) 119–162. [Google Scholar]
  25. D. Hinrichsen, A.J. Pritchard and S.B. Townley, Riccati equation approach to maximizing the complex stability radius by state feedback. Int. J. Control 52 (1990) 769–794. [CrossRef] [Google Scholar]
  26. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. II. Advanced theory and bundle methods. Vol. 306 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1993). [Google Scholar]
  27. A.D. Ioffe and V.M. Tihomirov, Theory of extremal problems. Vol. 6 of Stud. Math. Appl. Translated from the Russian by Karol Makowski. North-Holland Publishing Co., Amsterdam-New York (1979). [Google Scholar]
  28. C. Lemaréchal, The omnipresence of Lagrange. Ann. Oper. Res. 153 (2007) 9–27. [CrossRef] [Google Scholar]
  29. J.J. More, Generalizations of the trust region problem. Optimiz. Methods Softw. 2 (1993) 189–209. [CrossRef] [Google Scholar]
  30. A.A. Novotny and J. Sokołowski, Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer, Heidelberg (2013). [Google Scholar]
  31. S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  32. F. Rendl and H. Wolkowicz, A semidefinite framework for trust region subproblems with applications to large scale minimization. Semidefinite programming. Math. Program. Ser. B 77 (1997) 273–299. [Google Scholar]
  33. R.T. Rockafellar, Conjugate duality and optimization. Lectures given at the Johns Hopkins University, Baltimore, Md., June (1973), Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 16. Society for Industrial and Applied Mathematics, Philadelphia, Pa. (1974). [Google Scholar]
  34. J. Sokołowski and A. Żochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1251–1272. [CrossRef] [MathSciNet] [Google Scholar]
  35. D.C. Sorensen, Newton’s method with a model trust region modification. SIAM J. Numer. Anal. 19 (1982) 409–426. [CrossRef] [Google Scholar]
  36. R.J. Stern and H. Wolkowicz, Trust region problems and nonsymmetric eigenvalue perturbations. SIAM J. Matrix Anal. Appl. 15 (1994) 755–778. [CrossRef] [MathSciNet] [Google Scholar]
  37. R.J. Stern and H. Wolkowicz, Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5 (1995) 286–313. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.