An interior algorithm for nonlinear optimization that combines line search and trust region steps
- First Online:
An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed ineffective, a trust region iteration that guarantees progress toward stationarity is invoked. To demonstrate its effectiveness, the algorithm is implemented in the Knitro [6,28] software package and is extensively tested on a wide selection of test problems.
Unable to display preview. Download preview PDF.
- 1.Andersen, E.D., Gondzio, J., Mészáros, C., Xu, X.: Implementation of interior point methods for large scale linear programming. In: T. Terlaky, (ed.), Interior Point Methods in Mathematical Programming, Dordrecht, The Netherlands, 1996. Kluwer Academic Publishers, pp. 189–252Google Scholar
- 2.Betts, J., Eldersveld, S.K., Frank, P.D., Lewis, J.G.: An interior-point nonlinear programming algorithm for large scale optimization. Technical report MCT TECH-003, Mathematics and Computing Technology, The Boeing Company, P.O. Box 3707, Seattle WA 98124-2207, 2000Google Scholar
- 9.Conn, A.R., Gould, N.I.M., Toint, Ph.: Trust-region methods. MPS-SIAM Series on Optimization. SIAM publications, Philadelphia, Pennsylvania, USA, 2000Google Scholar
- 13.El-Hallabi, M.: A hybrid algorithm for nonlinear equality constrained optimization problems: global and local convergence theory. Technical Report TR4-99, Mathematics and Computer Science Department, Institut National des Postes et Télécommunications, Rabat, Morocco, 1999Google Scholar
- 14.Fletcher, R.: Practical Methods of Optimization. J. Wiley and Sons, Chichester, England, second edition, 1987Google Scholar
- 20.Harwell Subroutine Library. A catalogue of subroutines (HSL 2002). AEA Technology, Harwell, Oxfordshire, England, 2002Google Scholar
- 21.Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research. Springer, 1999Google Scholar
- 27.Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Technical Report RC 23149, IBM T.J. Watson Research Center, Yorktown Heights, NY, March 2004Google Scholar
- 28.Waltz, R.A., Nocedal, J.: KNITRO user's manual. Technical Report OTC 2003/05, Optimization Technology Center, Northwestern University, Evanston, IL, USA, April 2003Google Scholar
- 30.Yamashita, H.: A globally convergent primal-dual interior-point method for constrained optimization. Technical report, Mathematical System Institute, Inc., Tokyo, Japan, May 1992, Revised March 1994Google Scholar