The bordered operator and the index of a constrained critical point

Mathematische Nachrichten

Volumn 219, Issue , 2000, Pages 109-124

  Greenberg, Leon ^a   Maddocks, John H ^c   Hoffman, Kathleen A ^b  

^a University of Maryland   (United States)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^c EPFL   (Switzerland)

Author keywords

Constrained variational principle; Index; Isoperimetric conjugate point

Indexed keywords

EID: 0034355514     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200011)219:1<109::AID-MANA109>3.0.CO;2-1     Document Type: Article

References (23)

1. BERKOWITZ, J.: On the Discreteness of Spectra of Singular Sturm-Liouville Problems, Communications on Pure and Applied Mathematics XII (1959), 523-542
2. BOLZA, O.: Lectures on the Calculus of Variations, Chelsea Publishing Company, 1973
3. CHABRILLAC, Y., and CROUZEIX, J. P.: Definiteness and Semidefiniteness of Quadratic Forms Revisited, Linear Algebra Appl. 63 (1984), 283-292
4. COTTLE, R. W.: Manifestations of the Schur Complement, Linear Algebra Appl. 8 (1974) 189-211
5. GREENBERG, L.: A Prüfer Method for Calculating Eigenvalues of Self-Adjoint Systems of Ordinary Differential Equations, Part 1, Technical Report TR91-24, University of Maryland, 1991
6. HAN, S. P.: On the Hessian of Lagrangian and Second-Order Optimality Conditions, SIAM J. Control Optim. 24 (1986), 339-345
7. HASSELL, C., and REES, E.: The Index of a Constrained Critical Point, Amer. Math. Monthly 100 (8) (1993), 772-778
8. n, I. Morse Theory, Chebyshev Approximation, Peter Lang Verlag, 1983
9. JONGEN, H. TH., MÖBERT, T., RÜCKMANN, J.-J., and TAMMER, K.: On Inertia and Schur Complement in Optimization, Lin. Alg. Appl. 95 (1987), 97-109
10. KATO, T.: Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1984
11. LUENBERGER, D. G.: Linear and Nonlinear Programming, Addison-Wesley, 1989
12. MADDOCKS, J. H.: Restricted Quadratic Forms, Inertia Theorems, and the Schur Complement, Linear Algebra and Appl. 108 (1988), 1-36
13. MANN, H. B.: Quadratic Forms with Linear Constraints, Amer. Math. Monthly 50 (1943) 430-433
14. MANNING, R. S., ROGERS, K. A., and MADDOCKS, J. H.: Isoperimetric Conjugate Points and Stability of DNA Minicircles, Proc. R. Soc. Lond. A 454 (1998), 3047-3074
15. MILNOR, J.: Morse Theory, Ann. Math. Stud. Volume 51, Princeton University Press, 1963
16. MORSE, M.: The Calculus of Variations in the Large, Colloquium Publications Volume 18, American Mathematical Society, 1932
17. REED, M., and SIMON, B.: Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press, 1972
18. ROGERS, K. A.: Stability Exchange in Parameter-Dependent Constrained Variational Principles with Applications to Elastic Rod Models of DNA Minicircles, PhD Thesis University of Maryland, 1997
19. HOFFMAN, K. A., and MADDOCKS, J. H.: Distinguished Bifurcation Diagrams and the Stability of a Twisted Elastic Loop, preprint, 1998
20. SHUTLER, P.: Constrained Critical Points, American Math. Monthly 102(1) (1995), 49-52
21. SPRING, D.: On the Second Derivative Test for Constrained Local Extrema, Amer. Math. Monthly 92 (9) (1985), 631-643
22. WEIDMANN, J.: Spectral Theory of Ordinary Differential Operators. In: Lecture Notes in Mathematics Volume 1258, Springer-Verlag, Berlin-New York, 1987
23. WEINSTEIN, A., and STENGER, W.: Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications, Academic Press, 1972