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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Bibliographic Details
Published in:International journal of control Vol. 94; no. 11; pp. 2956 - 2979
Main Authors: Michalowsky, Simon, Scherer, Carsten, Ebenbauer, Christian
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2021
Taylor & Francis Ltd
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2020.1745286