A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point a...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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AMER INST MATHEMATICAL SCIENCES-AIMS
2020
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| Online Access: | http://hdl.handle.net/20.500.11937/91435 |
| _version_ | 1848765519867412480 |
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| author | Dai, Y.H. Liu, X.W. Sun, Jie |
| author_facet | Dai, Y.H. Liu, X.W. Sun, Jie |
| author_sort | Dai, Y.H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is ecient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. |
| first_indexed | 2025-11-14T11:36:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-91435 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:33Z |
| publishDate | 2020 |
| publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914352023-04-20T06:21:22Z A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs Dai, Y.H. Liu, X.W. Sun, Jie Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Nonlinear programming constrained optimization infeasibility interior-point method global and local convergence GLOBAL CONVERGENCE ALGORITHM OPTIMIZATION With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is ecient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. 2020 Journal Article http://hdl.handle.net/20.500.11937/91435 10.3934/jimo.2018190 English AMER INST MATHEMATICAL SCIENCES-AIMS fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Nonlinear programming constrained optimization infeasibility interior-point method global and local convergence GLOBAL CONVERGENCE ALGORITHM OPTIMIZATION Dai, Y.H. Liu, X.W. Sun, Jie A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title_full | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title_fullStr | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title_full_unstemmed | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title_short | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| title_sort | primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs |
| topic | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Operations Research & Management Science Mathematics, Interdisciplinary Applications Engineering Mathematics Nonlinear programming constrained optimization infeasibility interior-point method global and local convergence GLOBAL CONVERGENCE ALGORITHM OPTIMIZATION |
| url | http://hdl.handle.net/20.500.11937/91435 |