Research ArticleOpen AccessGoogle Scholar indexed
Global Convergence of a Modified Tri-Dimensional Filter Method
Department of Mathematics and Information Science, Hebei University, Baoding, China
Department of Mathematics and Information Science, Hebei University, Baoding, China
Department of Mathematics and Information Science, Hebei University, Baoding, China
- 1 Department of Mathematics and Information Science, Hebei University, Baoding, China
- 2 Department of Mathematics and Information Science, Hebei University, Baoding, China
- 3 Department of Mathematics and Information Science, Hebei University, Baoding, China
Applied Mathematics·Volume 06 (2015)·Pages 235–241·Published 3 February 2015·DOI10.4236/am.2015.62023
Copy link · social · email
Abstract
In this paper, a tri-dimensional filter method for nonlinear programming was proposed. We add a parameter into the traditional filter for relaxing the criterion of iterates. The global convergent properties of the proposed algorithm are proved under some appropriate conditions.
KeywordsTri-DimensionalNCP FunctionGlobal ConvergenceQP-Free
- Fletcher, R. and Leyyfer, S. (2002) Nonlinear Programming without a Penalty Function. Mathematical Programming, 91, 239-269. http://dx.doi.org/10.1007/s101070100244
- Fletcher, R., Leyffer, S. and Toint, P.L. (1998) On the Global Convergence of an SLP-Filter Algorithm. Numerical Analysis Report NA/183, University of Dundee, Dundee.
- Fletcher, R., Leyffer, S., et al. (2006) A Brief History of Filter Methods. Mathematics and Computer Science Division, Preprint ANL/MCSP1372-0906, Argonne National Laboratory.
- Chin, C.M., Rashid, A.H.A. and Nor, K.M. (2007) Global and Local Convergence of a Filter Line Search Method for Nonlinear Programming. Optimization Method Software, 22, 365-390. http://dx.doi.org/10.1080/10556780600565489
- Wang, X. (2010) A New Filter Trust Region Method for Nonlinear Programming. Journal of the Operations Research of China, 10, 133-140.
- Zhou, Y. and Pu, D. (2007) A New QP-Free Feasible Method for Inequality Constrained Optimization. OR Transactions, 11, 31-43.
- Curtis, F.E. and Nocedal, J.(2008) Flexible Penalty Function for Nonlinear Constrained Optimization. IMA Journal of Numerical Analysis, 28, 749-769. http://dx.doi.org/10.1093/imanum/drn003
- Su, K. (2008) A New Globally and Superlinearly Convergent QP-Free Method for Inequality Constrained Optimization. Journal of Tongji University, 36, 265-272.
- Pu, D.G., Li, K. and Xue, W. (2005) Convergence of QP-Free Infeasible Methods for Nonlinear Inequality Constrained Optimization Problems. Journal of Tongji University, 33, 525-529.