A trust region method based on interior point techniques for nonlinear programming

Mathematical Programming, Series B

Volumn 89, Issue 1, 2000, Pages 149-185

  Byrd, Richard H ^a   Gilbert, Jean Charles ^b   Nocedal, Jorge ^c  

^a UCB 450   (United States)

^b INRIA ROCQUENCOURT   (France)

^c NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Barrier method; Constrained optimization; Interior point method; Large scale optimization; Nonlinear programming; Primal method; Primal dual method; SQP iteration; Trust region method

Indexed keywords

EID: 0001130234     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011391     Document Type: Article

References (29)

1. Anstreicher, K.M., Vial, J.-P. (1994): On the convergence of an infeasible primal-dual interior-point method for convex programming. Optim. Methods Software 3, 273-283
2. Blanchon, G., Dodu, J.-C., Renaud, A., Bouhtou, M. (1996): Implementation of a primal-dual interior-point method applied to the planning of reactive power compensation devices. Proceedings of the 12th Power Systems Computation Conference, August 19-23, 1996, Dresden
3. Byrd, R.H. (1987): Robust trust region methods for constrained optimization. Talk given at the SIAM Conference on Optimization, Houston, TX, 1987
4. Byrd, R.H., Hribar, M.E., Nocedal, J. (1999): An interior point method for large scale nonlinear programming, SIAM J. Optim. 9, 877-900
5. Byrd, R.H., Liu, G., Nocedal, J. (1997): On the Local Behavior of an Interior Point Method for Nonlinear Programming. In: Griffiths, D.F., Higham, D.J., eds., Numerical Analysis 1997, pp. 37-56, Addison Wesley Longman
6. Byrd, R.H., Schnabel, R.B., Schultz, G.A. (1987): A trust region algorithm for nonlinearly constrained optimization. SIAM J. Numer. Anal. 24, 1152-1170
7. Cells, M.R., Dennis, J.E., Tapia, R.A. (1985): A trust region strategy for nonlinear equality constrained optimization. In: Boggs, P.T., Byrd, R.H., Schnabel, R.B., eds., Numerical Optimization 1984, SIAM, Philadelphia, pp. 71-82
8. Coleman, T.F., Li, Y. (1996): An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6(2), 418-445
9. Dennis, J.E., Heinkenschloss, M., Vicente, L.N. (1994): Trust-region interior-point SQP algorithms for a class of nonlinear programming problems. SIAM J. Control Optim. 36(5), 1750-1794
10. El-Bakry, A.S., Tapia, R.A., Tsuchiya, T., Zhang, Y. (1995): On the formulation and theory of the Newton interior-point method for nonlinear programming. J. Optim. Theory App. 89, 507-545
11. Fletcher, R. (1987): Practical Methods of Optimization (second edition). John Wiley & Sons, New York
12. Gill, P.E., Murray, W., Wright, M.H. (1981): Practical Optimization. Academic Press, London
13. Gonzaga, C.C. (1992): Path-following methods for linear programming. SIAM Rev. 34, 167-224
14. Granville, S. (1994): Optimal reactive dispatch through interior point methods. IEEE Trans. Power Systems 9, 136-146
15. Herskovits, J. (1998): Feasible direction interior-point technique for nonlinear optimization. J. Optim. Theory Appl. 99(1), 121-146
16. Hribar, M.B. (1997): Methods for Large-Scale Nonlinear Programming and Nonlinear Systems of Equations. Dissertation, Ph.D., EECS Department, Northwestern University
17. Jarre, F., Saunders, M. (1995): A Practical Interior-point Method for Convex Programming. SIAM J. Optim. 5, 149-171
18. Lalee, M., Nocedal, J., Plantenga, T.D. (1998): On the implementation of an algorithm for large-scale equality constrained optimization. SIAM J. Optim. 8, 682-706
19. Lustig, I.J., Marsten, R.E., Shanno, D.F. (1994): Interior point methods for linear programming: Computational state of the art. ORSA J. Comput. 6, 1-14
20. Omojokun, E.O. (1991): Trust region algorithms for optimization with nonlinear equality and inequality constraints. Ph.D Dissertation, University of Colorado
21. Panier, E.R., Tits, A.L., Herskovits, J.N. (1988): A QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization. SIAM J. Control Optim. 26, 788-811
22. Plantenga, T.D. (1999): A trust region method for nonlinear programming based on primal interior point techniques. SIAM J. Sci. Comput. 20, 282-305
23. Powell, M.J.D. (1975): Convergence properties of a class of minimization algorithms. In: Mangasarian, O., Meyer, R., Robinson, S., eds., Nonlinear Programming 2, pp. 1-27, Academic Press, New York
24. Powell, M.J.D., Yuan, Y. (1991): A trust region algorithm for equality constrained optimization. Math. Program. 49, 189-211
25. Steihaug, T. (1983): The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626-637
26. Vardi, A. (1985): A trust region algorithm for equality constrained minimization: convergence properties and implementation. SIAM J. Numer. Anal. 22, 575-591
27. Wright, M.H. (1992): Interior methods for constrained optimization. Acta Numerica 1992, 341-407
28. Wu, Y.-C., Debs, A.S., Marsten, R.E. (1994): A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows. IEEE Trans. Power Systems 9, 876-883
29. Yamashita, H. (1992): A globally convergent primal-dual interior point method for constrained optimization. Technical Report, Mathematical Systems Institute Inc., Tokyo, Japan (Revised in March 1994)