A filter method for solving nonlinear complementarity problems
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| Title: | A filter method for solving nonlinear complementarity problems |
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| Authors: | Pu-yan Nie |
| Source: | Applied Mathematics and Computation. 167:677-694 |
| Publisher Information: | Elsevier BV, 2005. |
| Publication Year: | 2005 |
| Subject Terms: | 0211 other engineering and technologies, nonlinear complementarity problems, successive quadratic programming, Interior-point methods, 02 engineering and technology, numerical results, composite-like methods, Methods of successive quadratic programming type, global convergence, Numerical mathematical programming methods, interior point strategy, nonlinear programming, pattern search method, trust region method, multi-objective problems, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Multi-objective and goal programming, filter methods |
| Description: | Filter methods are extensively studied to handle nonlinear programming problems recently. Filter strategies do very well to balance the objective function and constraint conditions. Because of good numerical results, filter methods have been combined with trust region approaches, successive quadratic programming (SQP) techniques, pattern search method, interior point strategy and composite-like methods. In the work of \textit{S. Ulbrich} [Math. Program. 100, 217--245 (2004; Zbl 1146.90525)], super-linear local convergence is achieved for filter-SQP methods. In this work, filter methods are used to deal with the system of nonlinear complementarity problem (NCP). First, NCP conditions are transformed into a nonlinear programming problem. Then, to obtain a trial step, the corresponding nonlinear programming problems are solved by some existing strategies. In the filter method, at each step, after a subproblem is solved, the filter criterion is employed to determine whether to accept the trial point or not. In essence, multi-objective view is utilized to attack NCPs because the idea of filter methods stems from multi-objective problems. Furthemore, a new filter method based on special two objects which differs from others, is brought forward. Moreover, Maratos effects are overcome in our new filter approach by weakening acceptable conditions. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2004.06.125 |
| Access URL: | https://www.sciencedirect.com/science/article/pii/S0096300304005235 http://dblp.uni-trier.de/db/journals/amc/amc185.html#LongMN07 https://dblp.uni-trier.de/db/journals/amc/amc167.html#Nie05 |
| Rights: | Elsevier TDM |
| Accession Number: | edsair.doi.dedup.....6743690541d891bc0ef0d3b51a9c74ba |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | Filter methods are extensively studied to handle nonlinear programming problems recently. Filter strategies do very well to balance the objective function and constraint conditions. Because of good numerical results, filter methods have been combined with trust region approaches, successive quadratic programming (SQP) techniques, pattern search method, interior point strategy and composite-like methods. In the work of \textit{S. Ulbrich} [Math. Program. 100, 217--245 (2004; Zbl 1146.90525)], super-linear local convergence is achieved for filter-SQP methods. In this work, filter methods are used to deal with the system of nonlinear complementarity problem (NCP). First, NCP conditions are transformed into a nonlinear programming problem. Then, to obtain a trial step, the corresponding nonlinear programming problems are solved by some existing strategies. In the filter method, at each step, after a subproblem is solved, the filter criterion is employed to determine whether to accept the trial point or not. In essence, multi-objective view is utilized to attack NCPs because the idea of filter methods stems from multi-objective problems. Furthemore, a new filter method based on special two objects which differs from others, is brought forward. Moreover, Maratos effects are overcome in our new filter approach by weakening acceptable conditions. |
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| ISSN: | 00963003 |
| DOI: | 10.1016/j.amc.2004.06.125 |