Active sets, nonsmoothness, and sensitivity

SIAM Journal on Optimization

Volumn 13, Issue 3, 2003, Pages 702-725

  Lewis, A S ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Active set; Eigenvalue optimization; Generalized gradient; Identifiable surface; Nonsmooth analysis; Sensitivity; Spectral abscissa; Subdifferential; U Lagrangian

Indexed keywords

EID: 0042031309     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401387623     Document Type: Article

References (26)

1. K. D. ANDERSON, E. CHRISTIANSEN, A. R. CONN, AND M. L. OVERTON, An efficient primal-dual interior-point method for minimizing a sum of Euclidean norms, SIAM J. Sci. Comput., 22 (2000), pp. 243-262.
2. V. I. ARNOLD, On matrices depending on parameters, Russian Math. Surveys, 26 (1971), pp. 29-43.
3. A. BEN-TAL AND A. NEMIROVSKI, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia, 2001.
4. J. F. BONNANS AND A. SHAPIRO, Perturbation Analysis of Optimization Problems, Springer, New York, 2000.
5. J. V. BURKE, A. S. LEWIS, AND M. L. OVERTON, Optimal stability and eigenvalue multiplicity, Found. Comput. Math., 1 (2001), pp. 205-225.
6. P. H. CALAMAI AND A. R. CONN, A stable algorithm for solving the multifacility location problem involving Euclidean distances, SIAM J. Sci. Stat. Comput., 1 (1980), pp. 512-526.
7. p norm location problems, Math. Programming, 38 (1987), pp. 75-109.
8. A. V. FIACCO AND G. P. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, New York, 1968; reprinted, SIAM, Philadelphia, 1990.
9. R. FLETCHER, Practical Methods of Optimization, 2nd ed., Wiley, Chichester, UK, 1987.
10. R. A. HORN AND C. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
11. T. KATO, A Short Introduction to Perturbation Theory for Linear Operators, Springer, New York, 1982.
12. C. LEMARÉCHAL, F. OUSTRY, AND C. SAGASTIZÁBAL, The U-Lagrangian of a convex function, Trans. Amer. Math. Soc., 352 (2000), pp. 711-729.
13. C. LEMARÉCHAL AND C. SAGASTIZÁBAL, Practical aspects of the Moreau - Yosida regularization: Theoretical preliminaries, SIAM J. Optim., 7 (1997), pp. 367-385.
14. A. S. LEWIS AND M. L. OVERTON, Eigenvalue optimization, Acta Numer., 5 (1996), pp. 149-190.
15. R. MIFFLIN AND C. SAGASTIZÁBAL, Proximal Points Are on the Fast Track, Technical report, Washington State University, Pullman, WA, 2000.
16. Y. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, 1994.
17. M. R. OSBORNE, Simplicial Algorithms for Minimizing Polyhedral Functions, Cambridge University Press, Cambridge, UK, 2001.
18. F. OUSTRY, The U-Lagrangian of the maximum eigenvalue function, SIAM J. Optim., 9 (1999), pp. 526-549.
19. F. OUSTRY, A second-order bundle method to minimize the maximum eigenvalue function, Math. Program., 89 (2000), pp. 1-33.
20. M. L. OVERTON, A quadratically convergent method for minimizing a sum of Euclidean norms, Math. Programming, 27 (1983), pp. 34-63.
21. M. L. OVERTON AND R. S. WOMERSLEY, Second derivatives for optimizing eigenvalues of symmetric matrices, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 697-718.
22. M. L. OVERTON AND X. YE, Towards second-order methods for structured nonsmooth optimization, in Advances in Optimization and Numerical Analysis, S. Gomez and J.-P. Hennart, eds., Kluwer, Amsterdam, 1994, pp. 97-109.
23. R. T. ROCKAFELLAR AND R. J.-B. WETS, Variational Analysis, Springer, Berlin, 1998.
24. A. SHAPIRO AND M. K. H. FAN, On eigenvalue optimization, SIAM J. Optim., 5 (1995), pp. 552-569.
25. I. VAISMAN, A First Course in Differential Geometry, Marcel Dekker, New York, 1984.
26. S. J. WRIGHT, Identifiable surfaces in constrained optimization, SIAM J. Control Optim., 31 (1993), pp. 1063-1079.