A superlinearly convergent sequential quadratically constrained quadratic programming algorithm for degenerate nonlinear programming

SIAM Journal on Optimization

Volumn 12, Issue 4, 2002, Pages 949-978

  Anitescu, Mihai ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Degenerate constraints; Quadratic constraints; Sequential quadratic programming; Superlinear convergence

Indexed keywords

EID: 0036433570     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499365309     Document Type: Article

References (30)

1. K. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, 1988.
2. M. Anitescu, Degenerate nonlinear programming with a quadratic growth condition, SIAM J. Optim., 10 (2000), pp. 1116-1135.
3. D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982.
4. D.P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, MA, 1995.
5. J.F. Bonnans, Local analysis of Newton-type methods for variational inequalities and nonlinear programming, Appl. Math. Optim, 29 (1994), pp. 161-186.
6. J.F. Bonnans and A. Ioffe, Second-order sufficiency and quadratic growth for nonisolated minima, Math. Oper. Res., 20 (1995), pp. 801-819.
7. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000.
8. I. Bongartz, A.R. Conn, N. Gould, and Ph.L. Toint, CUTE: Constrained and unconstrained testing environment, ACM Trans. Math. Software, 21 (1995), pp. 123-160.
9. T. Coleman and A. Verma, ADMIT-1: Automatic Differentiation and MATLAB Interface Toolbox, Technical report CS TR 98-1663, Department of Computer Science, Cornell University, Ithaca, NY, 1998.
10. A.V. Fiacco, Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, 1983.
11. R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, Chichester, UK, 1987.
12. R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Program., 91 (2002), pp. 239-270.
13. J. Gauvin, A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Math. Programming, 12 (1977), pp. 136-138.
14. J. Gauvin and J.W. Tolle, Differential stability in nonlinear programming, SIAM J. Control Optim., 15 (1977), pp. 294-311.
15. P.E. Gill, W. Murray, and M.A. Saunders, User's guide for SNOPT 5.3: A Fortran Package for Large-Scale Nonlinear Programming, Report NA 97-5, Department of Mathematics, University of California, San Diego, CA, 1997.
16. W.W. Hager, Stabilized sequential quadratic programming, Comput. Optim. Appl., 12 (1999), pp. 253-273.
17. W.W. Hager and M.S. Gowda, Stability in the presence of degeneracy and error estimation, Math. Program., 85 (1999), pp. 181-192.
18. A.J. Hoffman, On approximate solutions of systems of linear inequalities, J. Res. National Bureau of Standards, 49 (1952), pp. 263-265.
19. A.D. Ioffe, Necessary and sufficient conditions for a local minimum. 3: Second order conditions and augmented duality, SIAM J. Control Optim., 17 (1979), pp. 266-288.
20. A. Ioffe, On sensitivity analysis of nonlinear programs in Banach spaces: The approach via composite unconstrained optimization, SIAM J. Optim., 4 (1994), pp. 1-43.
21. S. Kruk and H. Wolkowicz, Sequential, quadratic constrained, quadratic programming for general nonlinear programming, in Handbook of Semidefinite Programming, H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds, Kluwer Academic Publishers, Boston, 2000, pp. 563-575.
22. O.L. Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969.
23. O.L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality constraints, J. Math. Anal. Appl., 17 (1967), pp. 34-47.
24. The NEOS Guide, available online at http://www.mcs.anl.gov/otc/Guide.
25. E. Polak, Optimization, Springer-Verlag, New York, 1997.
26. D. Ralph and S.J. Wright, Superlinear Convergence of an Interior-Point Method Despite Dependent Constraints, preprint ANL/MCS-P622-1196, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1996.
27. S.M. Robinson, Generalized equations and their solutions, Part II: Applications to nonlinear programming, Math. Programming Study, 19 (1980), pp. 200-221.
28. A. Shapiro, Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim., 26 (1988), pp. 628-645.
29. S.J. Wright, Superlinear convergence of a stabilized SQP method to a degenerate solution, Comput. Optim. Appl., 11 (1998), pp. 253-275.
30. S.J. Wright, Modifying SOP for Degenerate Problems, preprint ANL/MCS-P699-1097, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1997.