The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints
The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the...
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/430932 |
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| author | Zhengyong Zhou Bo Yu |
| author_facet | Zhengyong Zhou Bo Yu |
| author_sort | Zhengyong Zhou |
| collection | DOAJ |
| description | The aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the gradient and Hessian of the aggregate constraint function are complicated combinations of gradients and Hessians of all constraint functions, and hence they are expensive to calculate when the number of constraint functions is very large. In order to improve the performance of the aggregate constraint homotopy method for solving nonlinear programming problems, with few variables and many nonlinear constraints, a flattened aggregate constraint homotopy method, that can save much computation of gradients and Hessians of constraint functions, is presented. Under some similar conditions for other homotopy methods, existence and convergence of a smooth homotopy path are proven. A numerical procedure is given to implement the proposed homotopy method, preliminary computational results show its performance, and it is also competitive with the state-of-the-art solver KNITRO for solving large-scale nonlinear optimization. |
| format | Article |
| id | doaj-art-417be74d9f09498e9189eebf0881ea0b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-417be74d9f09498e9189eebf0881ea0b2025-02-03T01:09:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/430932430932The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear ConstraintsZhengyong Zhou0Bo Yu1School of Mathematics and Computer Sciences, Shanxi Normal University, Linfen, Shanxi 041004, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, ChinaThe aggregate constraint homotopy method uses a single smoothing constraint instead of m-constraints to reduce the dimension of its homotopy map, and hence it is expected to be more efficient than the combined homotopy interior point method when the number of constraints is very large. However, the gradient and Hessian of the aggregate constraint function are complicated combinations of gradients and Hessians of all constraint functions, and hence they are expensive to calculate when the number of constraint functions is very large. In order to improve the performance of the aggregate constraint homotopy method for solving nonlinear programming problems, with few variables and many nonlinear constraints, a flattened aggregate constraint homotopy method, that can save much computation of gradients and Hessians of constraint functions, is presented. Under some similar conditions for other homotopy methods, existence and convergence of a smooth homotopy path are proven. A numerical procedure is given to implement the proposed homotopy method, preliminary computational results show its performance, and it is also competitive with the state-of-the-art solver KNITRO for solving large-scale nonlinear optimization.http://dx.doi.org/10.1155/2014/430932 |
| spellingShingle | Zhengyong Zhou Bo Yu The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints Abstract and Applied Analysis |
| title | The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints |
| title_full | The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints |
| title_fullStr | The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints |
| title_full_unstemmed | The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints |
| title_short | The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonlinear Constraints |
| title_sort | flattened aggregate constraint homotopy method for nonlinear programming problems with many nonlinear constraints |
| url | http://dx.doi.org/10.1155/2014/430932 |
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