Relative Lipschitz-like property of parametric systems via projectional coderivative
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916449062223872 |
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| author | Yao, Wenfang Yang, Xiaoqi |
| author_facet | Yao, Wenfang Yang, Xiaoqi |
| contents | This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The equivalence between the relative Lipschitz-like property and the local inner-semicontinuity for polyhedral multifunctions is also demonstrated. For the solution mapping of linear complementarity problems with a $Q_0$-matrix, we establish a sufficient and necessary condition for the Lipschitz-like property relative to its convex domain via the generalized critical face condition and its combinatorial nature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_11335 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Relative Lipschitz-like property of parametric systems via projectional coderivative Yao, Wenfang Yang, Xiaoqi Optimization and Control 49J40, 49J53, 49K40, 90C31, 90C33 This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The equivalence between the relative Lipschitz-like property and the local inner-semicontinuity for polyhedral multifunctions is also demonstrated. For the solution mapping of linear complementarity problems with a $Q_0$-matrix, we establish a sufficient and necessary condition for the Lipschitz-like property relative to its convex domain via the generalized critical face condition and its combinatorial nature. |
| title | Relative Lipschitz-like property of parametric systems via projectional coderivative |
| topic | Optimization and Control 49J40, 49J53, 49K40, 90C31, 90C33 |
| url | https://arxiv.org/abs/2210.11335 |