Global Convergence of a Modified Tri-Dimensional Filter Method
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.
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.
Cite this paper
Gao, B. , Su, K. and Rong, Z. (2015) Global Convergence of a Modified Tri-Dimensional Filter Method. Applied Mathematics, 6, 235-241. doi: 10.4236/am.2015.62023.
Gao, B. , Su, K. and Rong, Z. (2015) Global Convergence of a Modified Tri-Dimensional Filter Method. Applied Mathematics, 6, 235-241. doi: 10.4236/am.2015.62023.
References
[1] Fletcher, R. and Leyyfer, S. (2002) Nonlinear Programming without a Penalty Function. Mathematical Programming, 91, 239-269.
http://dx.doi.org/10.1007/s101070100244 [2] 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. [3] 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. [4] 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 [5] Wang, X. (2010) A New Filter Trust Region Method for Nonlinear Programming. Journal of the Operations Research of China, 10, 133-140. [6] Zhou, Y. and Pu, D. (2007) A New QP-Free Feasible Method for Inequality Constrained Optimization. OR Transactions, 11, 31-43. [7] 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 [8] Su, K. (2008) A New Globally and Superlinearly Convergent QP-Free Method for Inequality Constrained Optimization. Journal of Tongji University, 36, 265-272. [9] 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.
[1] Fletcher, R. and Leyyfer, S. (2002) Nonlinear Programming without a Penalty Function. Mathematical Programming, 91, 239-269.
http://dx.doi.org/10.1007/s101070100244 [2] 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. [3] 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. [4] 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 [5] Wang, X. (2010) A New Filter Trust Region Method for Nonlinear Programming. Journal of the Operations Research of China, 10, 133-140. [6] Zhou, Y. and Pu, D. (2007) A New QP-Free Feasible Method for Inequality Constrained Optimization. OR Transactions, 11, 31-43. [7] 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 [8] Su, K. (2008) A New Globally and Superlinearly Convergent QP-Free Method for Inequality Constrained Optimization. Journal of Tongji University, 36, 265-272. [9] 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.