A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties

SIAM Journal on Optimization

Volumn 14, Issue 1, 2004, Pages 173-199

  Tits, André L ^a   Wächter, Andreas ^b   Bakhtiari, Sasan ^a   Urban, Thomas J ^c   Lawrence, Craig T ^d  

^a UNIVERSITY OF MARYLAND   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c JOHNS HOPKINS UNIVERSITY   (United States)

^d Alphatech   (United States)

Author keywords

Constrained optimization; Feasibility; Nonlinear programming; Primal dual interior point methods

Indexed keywords

EID: 1542291020     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401392123     Document Type: Article

References (28)

1. S. BAKHTIARI AND A.L. TITS, A simple primal-dual feasible interior-point method for nonlinear programming with monotone descent, Comput. Optim. Appl., 25 (2003), pp. 17-38.
2. J.V. BURKE, A robust trust region method for constrained nonlinear programming problems, SIAM J. Optim., 2 (1992), pp. 325-347.
3. R.H. BYRD, J.C. GILBERT, AND J. NOCEDAL, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89 (2000), pp. 149-185.
4. R.H. BYRD, M.E. HRIBAR, AND J. NOCEDAL, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9 (1999), pp. 877-900.
5. A.S. EL-BAKRY, R.A. TAPIA, T. TSUCHIYA, AND Y. ZHANG, On the formulation and theory of the Newton interior-point method for nonlinear programming, J. Optim. Theory Appl., 89 (1996), pp. 507-541.
6. A.V. FIACCO AND G.P. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, New York, 1968.
7. A. FORSGREN AND P.E. GILL, Primal-dual interior methods for nonconvex nonlinear programming, SIAM J. Optim., 8 (1998), pp. 1132-1152.
8. D.M. GAY, M.L. OVERTON, AND M.H. WRIGHT, A primal-dual interior method for nonconvex nonlinear programming, in Advances in Nonlinear Programming, Y. Yuan, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, pp. 31-56.
9. N.I.M. GOULD, D. ORBAN, AND PH.L. TOINT, CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, Revisited, Technical report TR/PA/01/04, CERFACS, Toulouse, France, 2001.
10. J.N. HERSKOVITS, Développement d'une Méthode Numérique pour l'Optimization Non-Linéaire, Ph.D. thesis, Université Paris IX - Dauphine, Paris, France, 1982.
11. J.N. HERSKOVITS, A two-stage feasible directions algorithm for nonlinear constrained optimization, Math. Program., 36 (1986), pp. 19-38.
12. W. HOCK AND K. SCHITTKOWSKI, Test Examples for Nonlinear Programming Codes, Lecture Notes in Econom. and Math. Systems 187, Springer-Verlag, Berlin, New York, 1981.
13. C.T. LAWRENCE AND A.L. TITS, Nonlinear equality constraints in feasible sequential quadratic programming, Optim. Methods Softw., 6 (1996), pp. 265-282.
14. N. MARATOS, Exact Penalty Function Algorithms for Finite Dimensional and Optimization Problems, Ph.D. thesis, Imperial College of Science and Technology, University of London, London, UK, 1978.
15. D.Q. MAYNE AND E. POLAK, Feasible direction algorithms for optimization problems with equality and inequality constraints, Math. Program., 11 (1976), pp. 67-80.
16. D.Q. MAYNE AND E. POLAK, A superlinearly convergent algorithm for constrained optimization problems, Math. Program. Stud., 16 (1982), pp. 45-61.
17. E.R. PANIER, A.L. TITS, AND J.N. HERSKOVITS, A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J. Control Optim., 26 (1988), pp. 788-811.
18. E. POLAK AND A.L. TITS, On globally stabilized quasi-Newton methods for inequality constrained optimization problems, in Proceedings of the 10th IFIP Conference on System Modeling and Optimization, New York, 1981, Lecture Notes in Control and Inform. Sci. 38, R.F. Drenick and E.F. Kozin, eds., Springer-Verlag, Berlin, 1982, pp. 539-547.
19. M. SAHBA, Globally convergent algorithm for nonlinearly constrained optimization problems, J. Optim. Theory Appl., 52 (1987), pp. 291-309.
20. S. SEGENREICH, N. ZOUAIN, AND J.N. HERSKOVITS, An optimality criteria method based on slack variables concept for large structural optimization, in Proceedings of the Symposium on Applications of Computer Methods in Engineering, Los Angeles, 1977, pp. 563-572.
21. A.L. TITS AND J.L. ZHOU, A simple, quadratically convergent algorithm for linear and convex quadratic programming, in Large Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn, and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994, pp. 411-427.
22. R.J. VANDERBEI AND D.F. SHANNO, An interior-point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl., 13 (1999), pp. 231-252.
23. A. WÄCHTER AND L.T. BIEGLER, Failure of global convergence for a class of interior point methods for nonlinear programming, Math. Program., 88 (2000), pp. 565-574.
24. A. WÄCHTER AND L.T. BIEGLER, Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming, Technical report CAPD B-01-09, Carnegie Mellon University, Pittsburgh, PA, 2001.
25. H. YABE AND H. YAMASHITA, Q-superlinear convergence of primal-dual interior point quasi-newton methods for constrained optimization, J. Oper. Res. Soc. Japan, 40 (1997), pp. 415-436.
26. H. YAMASHITA, A globally convergent primal-dual interior point method for constrained optimization, Optim. Methods Softw., 10 (1998), pp. 443-469.
27. H. YAMASHITA, H. YABE, AND T. TANABE, A Globally and Superlinearly Convergent Primal-Dual Interior Point Trust Region Method for Large Scale Constrained Optimization, Technical report, Mathematical Systems, Inc., Tokyo, Japan, 1998.
28. Y. YUAN, On the convergence of a new trust region algorithm, Numer. Math., 70 (1995), pp. 515-539.