セメリス アンドレアス（セメリス アンドレアス） | データ更新日：2023.06.15 |

准教授 ／
システム情報科学研究院
電気システム工学部門

**学会発表等**

1. | Andreas Themelis, Puya Latafat, Silvia Villa, Panagiotis Patrinos, Adaptive proximal gradient methods for convex bilevel optimization, Control & Optimisation (ContrOpt) Pisa 2023, 2023.05, [URL], Bilevel optimization is a comprehensive framework that bridges single- and multi-objective optimization. It encompassess many general formulations, such as, but not limited to, standard nonlinear programs. This work demonstrates how elementary proximal gradient iterations can be used to solve a wide class of convex bilevel optimization problems without involving subroutines. Compared to and improving upon existing methods, ours (1) can handle a much wider class of problems, including both constraints and nonsmooth terms, (2) does not require strong convexity or Lipschitz smoothness assumptions, and (3) provides a systematic adaptive stepsize selection strategy with no need of function evaluations. A linesearch-free variant is also proposed that eliminates wasteful backtracking trials at the sole expense of cost evaluations.. |

2. | Andreas Themelis, Ziyuan Wang, Hongjia Ou, Xianfu Wang, Inertia and relative smoothness in nonconvex minimization: a case study on the forward-reflected-backward algorithm, 2022 International Workshop on Continuous Optimization, 2022.12, [URL], The use of momentum to accelerate convergence of first-order algorithms has been gaining renewed interest ever since its first appearance 60 years back. Initially inspired by the physics intuition that inertia is effective in preventing oscillatory behaviors, momentum-type techniques are typically designed in attempt to improve convergence speed. While this effect can only be achieved and justified for positive momentum coefficients, our study on the forward-reflected-backward splitting of Malitsky and Tam suggests the necessity of "negative" values to guarantee convergence under mere relative smoothness assumptions, for nonconvex problems. Our conclusions are in line with, and more pessimistic than, a similar conjecture of Dragomir et al. for the mirror descent algorithm.. |

3. | Andreas Themelis, Splitting algorithms for nonconvex optimization: unified analysis and Newton-type acceleration, Northwestern Polytechnical University Optimization Seminar, 2022.10, We provide a unified interpretation of splitting algorithms for nonconvex optimization through the lens of majorization-minimization. Possibly under assumptions to compensate the lack of convexity, this setting is general enough to cover ADMM as well as forward-backward, Douglas-Rachford and Davis-Yin splittings. Proximal envelopes, a generalization of the Moreau envelope, are shown to be natural merit functions for establishing convergence results. Their regularity properties also enable the integration of fast direction of quasi-Newton-type, that differently from any other approach for nonsmooth optimization preserve the same operation complexity of the original splitting scheme.. |

4. | Andreas Themelis, Puya Latafat, Masoud Ahookhosh, Panagiotis Patrinos, Bregman proximal algorithms for composite and finite-sum nonconvex minimization problems, SIAM Conference on Optimization (OP21), 2021.07, [URL], The employment of Bregman divergences in splitting algorithms has been growing in popularity in the last few years. Firstly, the extra degree of freedom in the metric selection can lead to new algorithms or may provide new insights on known ones. Secondly, while many classical such schemes are bound to Lipschitz differentiability requirements (especially in the nonconvex setting), the recently introduced notion of ``relative smoothness'' has considerably widened the range of problems that can be addressed. This talk deals with Bregman proximal algorithms in the fully nonconvex setting. The employment of the Bregman Moreau envelope as Lyapunov function leads to extremely simple and intuitive converge analyses that naturally extend to block-coordinate variants. Furthermore, continuity of the envelope allows one to design linesearch-type extensions that preserve oracle complexity and convergence properties of first-order (Bregman) splitting schemes, and yet can attain up to superlinear asymptotic rates when directions of quasi-Newton type are selected.. |

5. | Andreas Themelis, Efficient lightweight solvers for real-time embedded nonlinear MPC, 60th SICE Annual Conference 2021, 2021.09, [URL], Model predictive control (MPC) has become a popular strategy to implement feedback control loops for a variety of systems. Since most systems are nonlinear by nature, nonlinear MPC offers a more accurate modeling, but it leads to nonconvex and much more complicated problems that need to be solved at every sampling step. In "embedded" applications such as autonomous driving, the resulting problems easily become of large scale and the sampling time can be as low as few milliseconds, thus imposing an imperative demand for algorithmic speed and efficiency. In this talk we show how the scalability properties of "proximal algorithms" can conveniently be employed to design certifiable, fast, and lightweight algorithms perfectly suited for embedded applications.. |

6. | Andreas Themelis, Optimization for real-time control with limited resources, 6th IFAC Conference on Engine and Powertrain Control, Simulation and Modeling, 2021.08, [URL], Model predictive control (MPC) has become a popular strategy to implement feedback control loops for a variety of systems. An MPC strategy aims at repeatedly selecting control inputs that yield the best outcome among all possible choices. To assess the quality of an input, a cost function is designed that takes into account the desired goals, such as going from point A to point B in short time without wasting fuel. This leads to a problem formulation where the objective is the "minimization" of a cost function, encoding the desired goal, subject to constraints, which instead account for actuators limitations (e.g. maximum speed or power) as well as environmental impediments such as physical obstacles or speed limits. Most systems in nature and science evolve according to "nonlinear" laws, and this leads to the major challenge of nonsmooth and nonconvex problems that need to be solved within sampling time, that is, before a new control input needs to be fed again to the system. In "embedded" applications such as autonomous driving, the resulting problems easily become of large scale and the sampling time can be as low as few milliseconds, thus imposing an imperative demand for algorithmic speed and efficiency. In this talk we show how the scalability properties of "proximal algorithms" can conveniently be employed to design certifiable, fast, and lightweight algorithms perfectly suited for embedded applications.. |

7. | Andreas Themelis, Puya Latafat, Panagiotis Patrinos, A globally and superlinearly convergent algorithm for finding fixed points of nonexpansive operators, 50th Anniversary of the Center for Operations Research and Econometrics, 2016.05. |

8. | Andreas Themelis, Silvia Villa, Alberto Bemporad, Panagiotis Patrinos, Stochastic Gradient Methods for Stochastic Model Predictive Control, 15th IEEE European Control Conference, 2016.06. |

9. | Andreas Themelis, Silvia Villa, Panagiotis Patrinos, Alberto Bemporad, A variable metric Stochastic Gradient method for large scale optimization, 28th European Conference on Operational Research, 2016.07. |

10. | Andreas Themelis, Puya Latafat, Panagiotis Patrinos, Newton-type operator splitting algorithms, 4th European Conference on Computational Optimization, 2016.09. |

11. | Andreas Themelis, Newton-type proximal algorithms for nonconvex optimization, LCCC focus period on large scale and distributed optimization, 2017.06. |

12. | Panagiotis Patrinos, Andreas Themelis, Accelerated Douglas-Rachford splitting and ADMM for structured nonconvex optimization, CMO-BIRS Workshop on Splitting Algorithms, Modern Operator Theory and Applications, 2017.09. |

13. | Lorenzo Stella, Andreas Themelis, Pantelis Sopasakis, Panagiotis Patrinos, A simple and efficient algorithm for Nonlinear MPC, 56th IEEE Conference on Decision and Control, 2017.12. |

14. | Andreas Themelis, Panagiotis Patrinos, Proximal envelopes, 17th IEEE European Control Conference, 2018.06. |

15. | Andreas Themelis, Panagiotis Patrinos, A universal majorization-minimization framework for the convergence analysis of nonconvex proximal algorithms, 6th International Conference on Continuous Optimization, 2019.08. |

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