2023 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 – 2025-03-31
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| Keywords | Optimization algorithms / Nonconvex optimization / Adaptive algorithms |
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| Outline of Annual Research Achievements |
The candidate obtained a one-year extension to smoothly transition to the next project on "adaptive" algorithms. Supervising a PhD student, a merging point was established on the integration of quasi-Newton stepsizes (this project) in adaptive schemes (next project) [1].
The finalization of this project is being achieved through a new window on IP methods [2], as part of an international collaboration with UBW Munich (DE).
Similar developments are expected from a visit of a student from UBC (CA), scheduled from June to August 2024.
[1] H Ou and A Themelis. Safeguarding adaptive methods: global convergence of Barzilai-Borwein and other stepsize choices, arXiv:2404.09617, 2024
[2] A De Marchi and A Themelis. An interior proximal gradient method for nonconvex optimization, arXiv:2208.00799, 2023
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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
The final deliverables of this project are being attained through an integration, not originally planned, of Newton-type proximal methods within a classical interior point framework [3]. The manuscript, based on the preliminary work [2], will be submitted to an international top-tier journal within the next month.
A new alley beyond local Lipschitz differentiability is also being investigated in the convex case [1, 4].
Several preprints have been published in the meantime.
[3] A De Marchi and A Themelis. A penalty barrier framework for nonconvex constrained optimization (work in progress, soon to be submitted)
[4] K Oikonomidis et al. Adaptive proximal gradient methods are universal without approximation, arXiv:2402.06271, 2024
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| Strategy for Future Research Activity |
Apart from ultimating ongoing works mentioned above, the candidate intends to publish an extended monograph for the Foundations and Trends in Optimization about his main research. Given the accomplishments of the other goals, this pending work can now resume without impediments.
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| Causes of Carryover |
(1) Because of COVID, in the first 1.5 years conferences I usually attend have been canceled or made online. Fees have been reduced and travel and accommodation expenses waived.
(2) After a collaboration with Prof. Wang from UBC, Canada (collaborator with NCU, China) last August I have been invited for a fully funded visiting at NCU, preventing me from attending other summer conferences.
(3) To boost productivity I have relied on international collaborations. The resulting work was often presented in Europe, and because of geographical convenience sometimes others have attended and presented.
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