2021 Fiscal Year Research-status Report
New-generation optimization algorithms for engineering
| Project/Area Number |
21K17710
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| Research Institution | Kyushu University |
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Principal Investigator |
Themelis Andreas 九州大学, システム情報科学研究院, 准教授 (50898749)
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | Optimization algorithms / Autonomous driving / Decentralized control / Nonconvex optimization |
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| Outline of Annual Research Achievements |
The candidate established a new and collaboration with the Bundeswehr University, Munich (DE). This resulted in [1], where the candidate jointly tackled two of the goals described in the proposal: overcoming stringent assumptions of Lipschitz differentiability in nonsmooth, fully nonconvex optimization, and developing practical augmented Lagrangian methods. In [2], the candidate developed new insights on nonconvex duality through the employment of Bregman distances. Also this prospect was considered in the proposal. In [3], the candidate developed new autonomous driving paradigms for swarms of vehicles, in collaboration with Prof. Yamamoto's lab. This collaboration too was part of the proposal.
[1] A De Marchi, AT. Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC. arXiv:2112.13000, 2021 (passed 1st review round on Journal of Optimization Theory and Applications)
[2] E Laude, AT, P Patrinos. Conjugate dualities for relative smoothness and strong convexity under the light of generalized convexity. arXiv:2112.08886, 2021 (under review in the SIAM Journal on Optimization)
[3] A Nag, S Huang, AT, K Yamamoto. Flock navigation with dynamic hierarchy and subjective weights using nonlinear MPC. arXiv:2202.11331, 2022 (submitted to the IEEE 2022 CCTA conference)
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
As briefly outlined in the summary of research achievement, the candidate believes that the project is progressing quite smoothly on most of the aspects therein considered. Admittedly, one possible fallback is the absence of related software development, which is however understandable at this early stage where establishing a solid theoretical ground is the priority.
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| Strategy for Future Research Activity |
The candidate is currently in the stage of writing an extended (>100 page) monograph on nonconvex optimization to be submitted to the Foundations and Trends in Optimization. This possibility was mentioned in the research proposal. The monograph aims both at developing the basic theory and techniques to deal with nonconvex problems and delving into deeper theoretical and practical aspects that comprise the intellectual property of the candidate's past and current research. The monograph is being written in a tutorial style, aiming at becoming a new reference text for junior PhD students. It shall nevertheless also contain advanced and novel results, thus targeting experienced audiences as well.
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| Causes of Carryover |
Because of COVID, some conferences have been canceled and others have been held only virtually. This resulted in lower attendance fees, and no travel expenses. This year I am already planning to present my work abroad, and I will start supervising a PhD student who will also benefit from part of this grant. I am also considering to host people from abroad with whom I am collaborating and/or travel to their institution for short periods.
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Research Products
(6 results)
