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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.05181 |
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| _version_ | 1866913837883588608 |
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| author | Lin, Kangyu Ohtsuka, Toshiyuki |
| author_facet | Lin, Kangyu Ohtsuka, Toshiyuki |
| contents | Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap penalty reformulation and then solves a sequence of gap penalty reformulations with an increasing penalty parameter. This study examines the convergence behavior of the new penalty method. We prove that it converges to a strongly stationary point of MPCC, provided that: (i) The MPCC linear independence constraint qualification holds. (ii) The upper-level strict complementarity condition holds. (iii) The gap penalty reformulation satisfies the second-order necessary conditions in terms of the second-order directional derivative. Because strong stationarity is used to identify the MPCC local minimum, our analysis indicates that the new penalty method can find an MPCC solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Gap Penalty Reformulation for Mathematical Programming with Complementarity Constraints: Convergence Analysis Lin, Kangyu Ohtsuka, Toshiyuki Optimization and Control Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap penalty reformulation and then solves a sequence of gap penalty reformulations with an increasing penalty parameter. This study examines the convergence behavior of the new penalty method. We prove that it converges to a strongly stationary point of MPCC, provided that: (i) The MPCC linear independence constraint qualification holds. (ii) The upper-level strict complementarity condition holds. (iii) The gap penalty reformulation satisfies the second-order necessary conditions in terms of the second-order directional derivative. Because strong stationarity is used to identify the MPCC local minimum, our analysis indicates that the new penalty method can find an MPCC solution. |
| title | A Gap Penalty Reformulation for Mathematical Programming with Complementarity Constraints: Convergence Analysis |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.05181 |