Convergence to second order stationary points in inequality constrained optimization

Mathematics of Operations Research

Volumn 23, Issue 3, 1998, Pages 746-766

  Facchinei, Francisco ^a   Lucidi, Stefano ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Inequality constrained optimization; KKT second order necessary conditions; LC1 function; Negative curvature direction; Penalty function

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

INEQUALITY CONSTRAINED OPTIMIZATION; PENALTY FUNCTION;

OPERATIONS RESEARCH;

EID: 0032131216     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.23.3.746     Document Type: Article

References (29)

1. Auslender, A. 1979, Penalty methods for computing points that satisfy second order necessary conditions. Math. Programming 17 229-238.
2. Bertsekas, D. P. 1982. Constrained Optimization and Lagrange Multiplier Methods Academic Press, New York.
3. Byrd, R. H., R. B. Schnabel, G. A. Shultz. 1987. A trust region algorithm for nonlinearly constrained optimization. SIAM J. Numerical Analysis 24 1152-1170.
4. Clarke, F. H. 1983. Optimization and Nonsmooth Analysis. John Wiley & Sons, New York.
5. Coleman, T. F., Y. Li. 1996. An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optimization 6 418-445.
6. _, W. Yuan. 1995. A new trust-region algorithm for equality constrained optimization. Report TR95-1477, Department of Computer Science, Cornell University, Ithaca, NY.
7. Conn, A. R., N. I M. Gould, Ph. L. Toint 1988. Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM J. Numerical Analysis 25 433-460
8. Contaldi, G., G. Di Pillo, S. Lucidi. 1993. A continuously differentiable exact penalty function for nonlinear programming problems with unbounded feasible set. Oper. Res. Letters 14 153-161.
9. Dennis, J. E., L. N. Vicente. 1994. On the convergence theory of trust-region-based algorithms for equality-constrained optimization. Report TR94-36, Department of Computational and Applied Mathematics, Rice University, Houston, TX.
10. Di Pillo, G 1994. Exact penalty methods. E. Spedicato, ed. Algorithms for Continuous Optimization. NATO ASI Series Vol. 434. Kluwer Academic Publishers, Dordrecht, 209-253.
11. _, L. Grippo. 1984. A class of continuously differentiable exact penalty function algorithms for nonlinear programming problems P. Toft Christensen, ed. System Modelling and Optimization. Springer Verlag, Berlin, 246-256.
12. _, _. 1985. A continuously differentiable exact penalty function for nonlinear programming problems with inequalty constraints. SIAM J. Control Optim. 23 72-84.
13. _. _. 1989 Exact penalty functions in constrained optimization. SIAM J. Control Optim. 27 1333-1360.
14. El-Alem, M. 1995. Convergence to a second-order point for a trust-region algorithm with a nonmonotonic penalty parameter for constrained optimization. Report TR995-28. Department of Computational and Applied Mathematics, Rice University, Houston, TX.
15. Facchinei, F., A. Fischer, C. Kanzow. to appear. On the accurate identification of active constraints. SIAM J. Optim.
16. _, S. Lucidi. to appear. Globally and quadratically convergent exact penalty based methods for inequality constrained problems.
17. Ferris, M. C., S. Lucidi, M. Roma. 1996. Nonmonotone curvilinear line search methods for unconstrained optimization. Computational Optim. Appl. 6 117-136.
18. Forsgren, A., W. Murray. 1997. Newton methods for large-scale linear inequality constrained minimization. SIAM J. Optim. 7 162-176.
19. Gill, Ph., W. Murray, M. Wright. 1981. Practical Optimization. Academic Press, New York.
20. 1 1 data. Appl. Math Optim. 11 43-56.
21. Lucidi, S. 1992. New results on a continuously differentiable exact penalty function. SIAM J. Optim. 2 558-574.
22. _, F. Rochetich, M. Roma. 1995. Curvilinear stabilization techniques for truncated Newton methods in large scale unconstrained optimization: The complete results. Report 02.95, Università di Roma "La Sapienza," Roma.
23. McCormick, G. P. 1977. A modification of Armijo's step-size rule for negative curvature. Math. Programming 13 111-115.
24. _. 1983. Nonlinear Programming: Theory, Algorithms and Applications. John Wiley & Sons, New York.
25. Moré, J J., D. C. Sorensen. 1979. On the use of directions of negative curvature in a modified Newton method. Math. Programming 16 1-20.
26. _, _. 1983. Computing a trust region step. SIAM J. Scientific Statist. Comput. 4 553-572.
27. Mukai, H., E. Polak. 1978. A second-order method for the general nonlinear programming problem. J. Optim. Theory Appl. 26 515-532.
28. Sorensen, D. C. 1982. Newton's method with a model trust region modification. SIAM J. Numerical Analysis 19 409-426.
29. Vicente, L. N. 1996. Trust-region interior-point algorithms for a class of nonlinear programming problems. Ph.D. thesis, Rice University, Houston, TX.