Free Access
Issue
ESAIM: M2AN
Volume 32, Number 2, 1998
Page(s) 153 - 175
DOI https://doi.org/10.1051/m2an/1998320201531
Published online 27 January 2017
  1. J. J. AUBERT and B. DACOROGNA: An example of a quasiconvex function that is not polyconvex in two dimensions, Arch. Rational Mech. Anal., 117, 155-166 (1992). [MR: 1145109] [Zbl: 0761.26009]
  2. F. ALUFFI-PENTINI, V. PARISI and F. ZIRILLI: Global optimization and stochastic differential equations, JOTA 47, 1-16 (1985). [MR: 802386] [Zbl: 0549.65038]
  3. G. AUBERT: Contribution aux problèmes du calcul des variations et applications à l'élasticité non linéaire, Thèse de doctorat, Paris VI (1986).
  4. J. M. BALL: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 64, 337-403 (1977). [MR: 475169] [Zbl: 0368.73040]
  5. J. M. BALL and F. MURAT: W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58, 225-253 (1984). [MR: 759098] [Zbl: 0549.46019]
  6. B. BRIGHI and M. CHIPOT: Approximated Convex Envelope of a Function, SIAM J. Numer. Anal. 31, 128-148 (1994). [MR: 1259969] [Zbl: 0796.65009]
  7. M. CHIPOT: Numerical analysis of oscillations in nonconvex problems, Numer. Math. 59, 747-767 (1991). [EuDML: 133577] [MR: 1128031] [Zbl: 0712.65063]
  8. M. CHIPOT and C. COLLINS: Numerical approximations in variational problems with potential wells, SIAM J. Numer. Anal. 29, 1002-1019 (1992). [MR: 1173182] [Zbl: 0763.65049]
  9. M. CHIPOT and V. LÉCUYER: Analysis and computations in the four-well problem, Preprint. [MR: 1422927] [Zbl: 0866.49031]
  10. C. COLLINS, D. KINDERLEHRER and M. LUSKIN: Numerical approximation of the solution of a variational problem with a double well potential, SIAM J. Numer. Anal. 28, 321-332 (1991). [MR: 1087507] [Zbl: 0725.65067]
  11. C. COLLINS and M. LUSKIN: Optimal order error estimates for the finite element approximation of the solution of a nonconvex variational problem, Math. Comp. 57, 621-637 (1991). [MR: 1094944] [Zbl: 0735.65042]
  12. B. DACOROGNA: Direct Methods in the Calculus of Variations, Berlin : Springer 1989. [MR: 990890] [Zbl: 0703.49001]
  13. B. DACOROGNA, J. DOUCHET, W. GANGBO and J. RAPPAZ: Some examples of rank one convex functions in dimension two, Proc. of Royal Soc. Edinburgh 114A, 135-150 (1990). [MR: 1051612] [Zbl: 0722.49018]
  14. B. DACOROGNA and J. P. HAEBERLY: Remarks on a Numerical Study of Convexity, Quasiconvexity and Rank One Convexity, in Progress in Nonlinear Differential Equations and Their Applications, vol. 25, pp. 143-154, R. Serapioni and F. Tomarelli, Eds., Basel: Birkhäuser 1996. [MR: 1414497] [Zbl: 0898.49012]
  15. B. DACOROGNA and J.-P. HAEBERLY: On Convexity Properties of Homogeneous Functions of Degree One, Proc. of Royal Soc. Edinburgh 126, 947-956 (1996). [MR: 1415815] [Zbl: 0895.49002]
  16. B. DACOROGNA and P. MARCELLINI: A counterexample in the vectorial calculus of variations, in Material instabilities in continuum mechanics, pp. 77-83, proceedings edited by J.-M. Ball, Oxford : Oxford Science Publc. 1988. [MR: 970519] [Zbl: 0641.49007]
  17. P. GILL, W. MURRAY and M. WRIGHT: Practical Optimization, London : Academic Press 1981. [MR: 634376] [Zbl: 0503.90062]
  18. P. A. GREMAUD: Numerical optimization and quasiconvexity, IMA Preprint Series #1133, University of Minnesota, April 1993. [MR: 1317874] [Zbl: 0824.65043]
  19. H. HARTWIG: A polyconvexity condition in dimension two, Proc. of Royal Soc. Edinburgh 125A, 901-910 (1995). [MR: 1361623] [Zbl: 0839.49013]
  20. T. IWANIEC and A. LUTOBORSKI: Integral estimates for null Lagrangian, Arch. Rational Mech. Anal.125, 25-79 (1993). [MR: 1241286] [Zbl: 0793.58002]
  21. D. C. LIU and J. NOCEDAL: On the limited memory BFGS method for large scale optimization, Math. Program. 45, 503-528 (1989). [MR: 1038245] [Zbl: 0696.90048]
  22. J. J. MORÉ and S. J. WRIGHT: Optimization Software Guide, Frontiers in Applied Mathematics 14, Philadelphia : SIAM 1993. [MR: 1245493] [Zbl: 0830.65050]
  23. C. B. MORREY: Quasiconvexity and the semicontinuity of multiple integrals, Pacific J. Math. 2, 25-53 (1952). [MR: 54865] [Zbl: 0046.10803]
  24. J. NOCEDAL: Theory of algorithms for unconstrained optimization, Acta Numerica, 199-242 (1991). [MR: 1165726] [Zbl: 0766.65051]
  25. M. OVERTON: On minimizing the maximum eigenvalue of a symmetric matrix, SIAM J. Matrix Anal. Appl. 9, 256-268 (1988). [MR: 938560] [Zbl: 0647.65044]
  26. M. OVERTON: Large-scale optimization of eigenvalues, SIAM J. Optim. 2, 88-120 (1992). [MR: 1147885] [Zbl: 0757.65072]
  27. W. H. PRESS, S. A. TEUKOLSKY, W. T. VETTERLING and B. P. FLANNERY: Numerical Recipes in C, 2nd ed., Cambridge: Cambridge University Press. 1992. [MR: 1201159] [Zbl: 0845.65001]
  28. F. F. SHANNO: Conjugate gradient methods with inexact searches, Math. Oper. Res. 3, 244-236 (1978). [MR: 506662] [Zbl: 0399.90077]
  29. D. F. SHANNO and K. H. PHUA : Remark on algorithm 500 : minimization of unconstrained multivariate functions, ACM Trans. on Math. Software 6, 618-622 (1980).
  30. V. SVERAK : Rank one convexity does not imply quasiconvexity, Proc. of Royal Soc. Edinburgh, 120A, 185-189 (1992). [MR: 1149994] [Zbl: 0777.49015]
  31. M. TOMASSlNI : A survey of genetic algorithms, to appear in Annual Reviews of Computational Physics, 3, World Scientific. [MR: 1415152]
  32. J. L. ZHOU and A. L. TITS : User's guide for FSQP version 3.4 (released December 1994), Systems Research Center TR-92-107r4, University of Maryland.

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