Robust and structure exploiting optimisation algorithms: an integral quadratic constraint approach

We consider the problem of analysing and designing gradient-based discrete-time optimisation algorithms for a class of unconstrained optimisation problems having strongly convex objective functions with Lipschitz continuous gradient. By formulating the problem as a robustness analysis problem and ma...

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Vydáno v:International journal of control Ročník 94; číslo 11; s. 2956 - 2979
Hlavní autoři: Michalowsky, Simon, Scherer, Carsten, Ebenbauer, Christian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 02.11.2021
Taylor & Francis Ltd
Témata:
algorithm design
Algorithms
Continuity (mathematics)
convex optimisation
Design optimization
Gradient-based optimisation algorithms
integral quadratic constraints (IQCs)
linear matrix inequalities (LMIs)
ISSN:0020-7179, 1366-5820
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Shrnutí:We consider the problem of analysing and designing gradient-based discrete-time optimisation algorithms for a class of unconstrained optimisation 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 analyse convergence rates and robustness properties of existing algorithms and enables the design of novel robust optimisation algorithms with prespecified guarantees capable of exploiting additional structure in the objective function.
Bibliografie:ObjectType-Article-1
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2020.1745286