Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization

Mathematical Programming, Series B

Volumn 75, Issue 3, 1996, Pages 377-397

  Yamashita, Hiroshi ^a   Yabe, Hiroshi ^b  

^a Mathematical Systems Institute Inc   (Japan)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

Interior point method; Local convergence; Nonlinear programming

Indexed keywords

EID: 0000273506     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02592190     Document Type: Article

References (23)

1. D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York, 1982).
2. C.G. Broyden, J.E. Dennis, Jr. and J.J. Moré, "On the local and superlinear convergence of quasi-Newton methods," Journal of the Institute of Mathematics and its Applications 12 (1973) 223-245.
3. J.E. Dennis, Jr. and J.J. Moré, "A characterization of superlinear convergence and its application to quasi-Newton methods," Mathematics of Computation 28 (1974) 549-560.
4. A.S. El-Bakry, R.A. Tapia, T. Tsuchiya and Y. Zhang, "On the formulation and theory of the primal-dual Newton interior-point method for nonlinear programming," TR92-40, Department of Computational and Applied Mathematics, Rice University, TX, USA, 1992.
5. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques (SIAM, Philadelphia, PA, 1990).
6. R. Fletcher, Practical Methods of Optimization (2nd ed., Wiley, New York, 1987).
7. D.M. Gay, "Electronic mail distribution of linear programming test problems," Mathematical Programming Society COAL Newsletter 13 (1985) 10-12.
8. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 187 (Springer-Verlag, Berlin, 1981).
9. M. Kojima, N. Megiddo and S. Mizuno, "A primal-dual infeasible-interior-point algorithm for linear programming," Mathematical Programming 61 (1993) 263-280.
10. M. Kojima, S. Mizuno and A. Yoshise, "A primal-dual interior-point algorithm for linear programming," in: N. Megiddo, ed., Progress in Mathematical Programming, Interior-Point and Related Methods (Springer-Verlag, New York, 1989) pp. 29-47.
11. L.S. Lasdon, J. Plummer and G. Yu, "Primal-dual and primal interior point algorithms for general nonlinear programs," Manuscript, 1993.
12. I.J. Lustig, R.E. Marsten and D.F. Shanno, "Computational experience with a primal-dual interior point method for linear programming," Linear Algebra and its Applications 152 (1991) 191-222.
13. G.P. McCormick, "Resolving the shell dual with a nonlinear primal-dual algorithm," Report GWU/OR/Serial T-545/91, Department of Operations Research, The George Washington University, Washington, DC, USA, 1991.
14. G.P. McCormick and J.E. Falk, "The superlinear convergence of a nonlinear primal-dual algorithm," Report GWU/OR/Serial T-550/91, Department of Operations Research, The George Washington University, Washington DC, USA, 1991.
15. K.A. McShane, C.L. Monma and D.F. Shanno, "An implementation of a primal-dual interior point method for linear programming," ORSA Journal on Computing 1 (1989) 70-83.
16. S. Mizuno, M.J. Todd and Y. Ye, "On adaptive step primal-dual interior-point algorithms for linear programming," Mathematics of Operations Reserch 18 (1993) 964-981.
17. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).
18. J.-P. Vial, "Computational experience with a primal-dual interior-point method for smooth convex programming," Optimization Methods and Software 3 (1994) 285-310.
19. H. Yamashita, "A globally convergent primal-dual interior point method for constrained optimization," Technical Report, Mathematical Systems Institute, Inc., Tokyo, Japan, 1992.
20. Y. Zhang, "On the convergence of a class of infeasible interior-point algorithms for the horizontal linear complementarity problem," SIAM Journal on Optimization 4 (1994) 208-227.
21. Y. Zhang and R.A. Tapia, "Superlinear and quadratic convergence of primal-dual interior point methods for linear programming revisited," Journal of Optimization Theory and Applications 73 (1992) 229-242.
22. Y. Zhang, R.A. Tapia and J.E. Dennis, Jr., "On the superlinear and quadratic convergence of primal-dual interior point linear programming algorithms," SIAM Journal on Optimization 2 (1992) 304-324.
23. Y. Zhang, R.A. Tapia and F. Potra, "On the superlinear convergence of interior point algorithms for a general class of problems," Technical Report TR90-9, Department of Mathematical Sciences, Rice University, TX, USA, 1990.