Finite Codimensionality Method in Infinite-dimensional Optimization Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912023061725184 |
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| author | Liu, Xu Lü, Qi Zhang, Haisen Zhang, Xu |
| author_facet | Liu, Xu Lü, Qi Zhang, Haisen Zhang, Xu |
| contents | This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization theory, a condition of finite codimensionality is employed to ensure the existence of nontrivial Lagrange multipliers. As applications, first-order necessary conditions for optimal control problems of some deterministic/stochastic control systems are derived in a unified manner. Compared with the existing constraint qualifications, the finite codimensionality condition, which is equivalent to some suitable {\it a priori} estimates, can offer a more straightforward verification process in these applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_00652 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Finite Codimensionality Method in Infinite-dimensional Optimization Problems Liu, Xu Lü, Qi Zhang, Haisen Zhang, Xu Optimization and Control 93B05, 49J20, 93B07, 49K20, 35Q93 This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization theory, a condition of finite codimensionality is employed to ensure the existence of nontrivial Lagrange multipliers. As applications, first-order necessary conditions for optimal control problems of some deterministic/stochastic control systems are derived in a unified manner. Compared with the existing constraint qualifications, the finite codimensionality condition, which is equivalent to some suitable {\it a priori} estimates, can offer a more straightforward verification process in these applications. |
| title | Finite Codimensionality Method in Infinite-dimensional Optimization Problems |
| topic | Optimization and Control 93B05, 49J20, 93B07, 49K20, 35Q93 |
| url | https://arxiv.org/abs/2102.00652 |