Robust and structure exploiting optimization algorithms: An integral quadratic constraint approach
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866914098734694400 |
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| author | Michalowsky, Simon Scherer, Carsten Ebenbauer, Christian |
| author_facet | Michalowsky, Simon Scherer, Carsten Ebenbauer, Christian |
| contents | We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By formulating the problem as a robustness analysis problem and making use of a suitable adaptation of the theory of integral quadratic constraints, we establish a framework that allows to analyze convergence rates and robustness properties of existing algorithms and enables the design of novel robust optimization algorithms with prespecified guarantees capable of exploiting additional structure in the objective function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_00279 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Robust and structure exploiting optimization algorithms: An integral quadratic constraint approach Michalowsky, Simon Scherer, Carsten Ebenbauer, Christian Optimization and Control Systems and Control We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By formulating the problem as a robustness analysis problem and making use of a suitable adaptation of the theory of integral quadratic constraints, we establish a framework that allows to analyze convergence rates and robustness properties of existing algorithms and enables the design of novel robust optimization algorithms with prespecified guarantees capable of exploiting additional structure in the objective function. |
| title | Robust and structure exploiting optimization algorithms: An integral quadratic constraint approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/1905.00279 |