Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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Springer
2004
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| Online Access: | http://hdl.handle.net/20.500.11937/91445 |
| _version_ | 1848765522655576064 |
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| author | Liu, X. Sun, Jie |
| author_facet | Liu, X. Sun, Jie |
| author_sort | Liu, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. © Springer-Verlag 2004. |
| first_indexed | 2025-11-14T11:36:35Z |
| format | Journal Article |
| id | curtin-20.500.11937-91445 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:35Z |
| publishDate | 2004 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914452023-04-20T04:34:24Z Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints Liu, X. Sun, Jie Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics global convergence interior-point methods mathematical programming with equilibrium constraints stationary point VARIATIONAL INEQUALITY CONSTRAINTS LINEAR COMPLEMENTARITY CONSTRAINTS OPTIMIZATION PROBLEMS BILEVEL ALGORITHM CONVERGENCE OPTIMALITY Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. © Springer-Verlag 2004. 2004 Journal Article http://hdl.handle.net/20.500.11937/91445 10.1007/s10107-004-0543-6 English Springer fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics global convergence interior-point methods mathematical programming with equilibrium constraints stationary point VARIATIONAL INEQUALITY CONSTRAINTS LINEAR COMPLEMENTARITY CONSTRAINTS OPTIMIZATION PROBLEMS BILEVEL ALGORITHM CONVERGENCE OPTIMALITY Liu, X. Sun, Jie Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title | Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title_full | Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title_fullStr | Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title_full_unstemmed | Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title_short | Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| title_sort | generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
| topic | Science & Technology Technology Physical Sciences Computer Science, Software Engineering Operations Research & Management Science Mathematics, Applied Computer Science Mathematics global convergence interior-point methods mathematical programming with equilibrium constraints stationary point VARIATIONAL INEQUALITY CONSTRAINTS LINEAR COMPLEMENTARITY CONSTRAINTS OPTIMIZATION PROBLEMS BILEVEL ALGORITHM CONVERGENCE OPTIMALITY |
| url | http://hdl.handle.net/20.500.11937/91445 |