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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.09208 |
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| _version_ | 1866913500151939072 |
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| author | Kiessling, David Leyffer, Sven Vanaret, Charlie |
| author_facet | Kiessling, David Leyffer, Sven Vanaret, Charlie |
| contents | We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Unified Funnel Restoration SQP Algorithm Kiessling, David Leyffer, Sven Vanaret, Charlie Optimization and Control Mathematical Software We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances. |
| title | A Unified Funnel Restoration SQP Algorithm |
| topic | Optimization and Control Mathematical Software |
| url | https://arxiv.org/abs/2409.09208 |