×

Nonmonotone trust-region method for nonlinear programming with general constraints and simple bounds. (English) Zbl 1129.90353

Summary: We propose a nonmonotone trust-region algorithm for the solution of optimization problems with general nonlinear equality constraints and simple bounds. Under a constant rank assumption on the gradients of the active constraints, we analyze the global convergence of the proposed algorithm.

MSC:

90C30 Nonlinear programming
90C55 Methods of successive quadratic programming type
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Schittkowski, K., The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian-Type Line Search Function, Numerische Mathematik, Vol. 38, pp. 83–114, 1981. · Zbl 0534.65030
[2] Chen, Z. W., Han, J. Y., and Han, Q. M., A Globally Convergent Trust-Region Algorithm for Optimization with General Constrains and Simple Bounds Acta Mathematicae Applicatae Sinica, Vol. 15, pp. 425–432, 1999. · Zbl 1052.90611
[3] Gomes, F. A. M., Maciel, M. C., and Martinez, J. M., Nonlinear Programming Algorithms Using Trust Regions and Augmented Lagrangians with Nonmonotone Penalty Parameters, Mathematical Programming, Vol. 84, pp. 161–200, 1999. · Zbl 1050.90574
[4] Conn, A. R., Gould, N. I. M., and Toint, P. L., Trust-Region Methods, MPS/SIAM Series on Optimization, 2000.
[5] Dennis, J., El-Alem, M. M., and Maciel M. C., A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization, SIAM Journal on Optimization Vol. 7, pp. 177–207, 1997. · Zbl 0867.65031
[6] El-Alem, M. M., A Global Convergence Theory for Dennis, El-Alem, and Maciel’s Class of Trust-Region Algorithms for Constrained Optimization without Assuming Regularity, SIAM Journal on Optimization, Vol. 9, pp. 965–990, 1999. · Zbl 0957.65059
[7] Byrd, R. H., Schnabel, R. B., and Schultz, G. A., A Trust-Region Algorithm for Nonlinearly Constrained Optimization, SIAM Journal on Numerical Analysis, Vol. 24, pp. 1152–1170, 1987. · Zbl 0631.65068
[8] Martinez, J. M., and Santos, S. A., A Trust-Region Strategy for Minimization on Arbitrary Domains, Mathematical Programming, Vol. 68, pp. 267–301, 1995. · Zbl 0835.90092
[9] MorĂ©, J. J., Recent Developments in Algorithms and Software for Trust-Region Methods, Mathematical Programming, The State of the Art, Springer, Berlin, German, pp. 258–287, 1983.
[10] omojokun, E. O., Trust-Region Algorithm for Optimization with Nonlinear Equality and Inequality Constrains, PhD Thesis, University of Colorado, Boulder, Colorado, 1989.
[11] Powell, M. J. D., and Yuan, Y., A Trust-Region Algorithm for Optimization with Equality Constrained Optimization, Mathematical Programming, Vol. 49. pp. 189–211, 1991. · Zbl 0816.90121
[12] Yuan, Y., On the Convergence of a New Trust-Region Algorithm, Numerische Mathematik, Vol. 70, pp. 515–539, 1995. · Zbl 0828.65062
[13] Toint, P. L., A Nonmonotone Trust-Region Algorithm for Nonlinear Optimization Subject to Convex Constraints, Mathematical Programming, Vol. 77. pp. 69–94, 1997. · Zbl 0891.90153
[14] Bonnans, J. F., Panier, E., Tits, A., and Zhou J. L., Avoiding the Maratos Effect by Means of a Nonmonotone Line Search, II: Inequality Constrained Problems-Feasible Iterates, SIAM Journal on Numerical Analysis, Vol. 29. pp. 1187–1202, 1992. · Zbl 0763.65042
[15] Deng, N. Y., Xiao, Y., and Zhou, F. J., A Nonmonotonic Trust-Region Algorithm, Journal of Optimization Theory and Applications, Vol. 76. pp. 259–285, 1993. · Zbl 0797.90088
[16] Facchinei, F., and Lucidi, S., Nonmonotone Bundle-Type Scheme for Convex Nonsmooth Minimization, Journal of Optimization Theory and Applications, Vol. 76, pp. 241–257, 1993. · Zbl 0802.49011
[17] Grippo, L., Lampariello, F., and Lucidi, S., A Nonmonotone Line Search Technique for Newton’s Method, SIAM Journal on Numerical Analysis, Vol. 23. pp. 707–716, 1986. · Zbl 0616.65067
[18] Grippo, L., Lampariello, F., and Lucidi, S., A Truncated Newton Method with Nonmonotone Line Search for Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 60. pp. 401–419, 1989. · Zbl 0632.90059
[19] Grippo, L., Lampariello, F., and Lucidi, S., A Class of Nonmonotone Stabilization Methods in Unconstrained Optimization, Numerische Mathematik, Vol. 59, pp. 779–805, 1991. · Zbl 0724.90060
[20] Ke, X. W., and Han, J. Y., Global Convergence of a Class of New Trust-Region Algorithms, Acta Mathematicae Applicatae Sinica, Vol. 18, pp. 608–615, 1995 (in Chinese). · Zbl 0857.65067
[21] Ke, X. W., and Han, J. Y., A Nonmonotonic Trust-Region Algorithm for Equality-Constrained Optimization, Science in China, Vol. 38A, pp. 683–695, 1995. · Zbl 0835.90089
[22] Ke, X. W., and Han, J. Y., A Class of Nonmonotone Trust-Region Algorithm for Constrained Optimization, Chinese Science Bulletin, Vol. 40, pp. 1321–1324, 1995. · Zbl 0856.90090
[23] Ke, X. W., and Han, J. Y., A Class of Nonmonotone Trust-Region Algorithm for Unconstrained Optimization, Science in China, Vol. 41A, pp. 927–932, 1998. · Zbl 0917.90271
[24] Ke, X. W., Liu, G. J., and Xu, D. C., A Class of Nonmonotone Trust-Region Algorithm for Unconstrained Optimization, Chinese Science Bulletin, Vol. 41, pp. 197–201, 1996. · Zbl 0846.90099
[25] Li, Z. F., and Deng, N. Y., A New Family of Nonmonotonic Trust-Region Algorithms and its Properties, Acta Mathematicae Applicatae Sinica, Vol. 22, pp. 457–465, 1999 (in Chinese). · Zbl 1052.90615
[26] Panier, E., and Tits, A., Avoiding the Maratos Effect by Means of a Nonmonotone Line Search, I: General Constrained Problems, SIAM Journal on Numerical Analysis, Vol. 28. pp. 1183–1195, 1991. · Zbl 0732.65055
[27] Toint, P. L., A Nonmonotonic Trust-Region Algorithm for Nonlinear Optimization Subject to Convex Constraints: Complete Numerical Results, Technical Report 94/26, Department of Mathematics, FUNDP, Namur, Belgium, 1994.
[28] Toint, P. L., An Assessment of Nonmonotone Line Search Techniques for Unconstrained Optimization, SIAM Journal on Scientific Computing, Vol. 17. pp. 725–739, 1996. · Zbl 0849.90113
[29] Chen, Z. W., Han, J. Y., and Xu, D. C., A Nonmonotonic Trust-Region Method for Nonlinear Programming with Simple Bound Constraints, Applied Mathematics and Optimization, Vol. 43. pp. 63–85, 2001. · Zbl 0973.65049
[30] Daniel, J. W., On Perturbations in Systems of Linear Inequalities, SIAM Journal on Numerical Analysis, Vol. 10. pp. 299–307, 1973. · Zbl 0268.90039
[31] Fletcher, R., Second-Order Corrections for Nondifferentiable Optimization, Numerical Analysis Proceedings, Dundee 1982; Lecture Notes in Mathematics, Edited by G. A. Watson, Springer, Berlin, Germany, Vol. 912, 1982.
[32] Hock, W., and Schittkowski, K., Test Examples for Nonlinear Programming Codes, Springer Verlag, Berlin, Germany, Vol. 187, 1981. · Zbl 0452.90038
[33] Schittkowski, K., More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, Vol. 282, 1987. · Zbl 0658.90060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.