Hayato Waki | Last modified date：2024.04.15 |

Graduate School

Undergraduate School

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Academic Degree

Doctor of science

Country of degree conferring institution (Overseas)

No

Field of Specialization

Optimization, Mathematical Programming, Continuous Optimization, Semidefinite Programming Problem, Optimization Software

Total Priod of education and research career in the foreign country

01years05months

Outline Activities

Optimization problem is the problem of finding the maximum or minimum of a given function over a given set, and is widely used in industry and daily life. My research interest are (i) to solve continuous optimization problems, e.g., convex optimization problems and semidefinite programming problems, (ii) to develop effective algorithms and software. In particular, I am strongly interested in research for solving nonlinear and nonconvex optimization problems by using convex optimization and semidefinite programming problems. Also, I research on the development of automotive engine control with industry-academia collaboration as IMI Joint Research.

Research

**Research Interests**

- Relationship between singularity degree of semidefinite program and the convergence rate of the alternating projection method

keyword : semidefinite program, singularity degree, alternating projection method, convergence rate

2020.04～2025.03. - We consider optimization modeling. In particular, we are interested in modeling with convex optimization.

Convex optimization is broadly used in various academic fields because it has a remarkable property that local solutions are also global.

We, however, often encounter ill-posedness in the resulting convex optimization problem. This means that the convex optimization problem

has no optimal solutions but, the objective value is finite. Then the computed solutions will be fragile and meaningless in practice.

We research how to model well-posed convex optimization from the various phenomena and/or to reveal why we encounter such an ill-posedness.

keyword : convex optimization, facial reduction

2017.04～2020.03. - Optimization problem is the problem of finding the maximum or minimum of a given function over a given set, and is widely used in industry and daily life. My research interest are (i) to solve continuous optimization problems, e.g., convex optimization problems and semidefinite programming problems, (ii) to develop effective algorithms and software. In particular, I am strongly interested in research for solving nonlinear and nonconvex optimization problems by using convex optimization and semidefinite programming problems. However, such problems have two difficulties: (1) the resulting convex optimization problems become too large-scale to handle, (2) the resulting problems become too degenerate to solve accurately. In addition, we often encounter phenomena that the theoretical results are completely different from computational results due to numerical errors, e.g., round-off errors in computation. Moreover, I am also interested in applications of optimization methods.

keyword : Optimization, mathematical programming, continuous optimization, semidefinite programming problem, optimization software

2012.04～2019.03.

**Academic Activities**

**Reports**

1. | Hayato Waki, Strict Feasibility of Conic Optimization Problems, Springer, https://doi.org/10.1007/978-4-431-55060-0_24, 2014.06, [URL]. |

**Papers**

1. | Hayato Waki, Yoshio Ebihara, Noboru Sebe, Reduction of SISO H-infinity Output Feedback Control Problem, Linear algebra and its applications, 2020.10, [URL]. |

2. | Hayato Waki, Noboru Sebe, Characterization of the dual problem of linear matrix inequality for H-infinity output feedback control problem via facial reduction, Mathematics of Control, Signals, and Systems, https://doi.org/10.1007/s00498-020-00261-z, 32, 361-384, 2020.07, [URL]. |

3. | Hayato Waki, Noboru Sebe, Reduction of H-infinity state feedback control problems for the MIMO servo systems, Asian Journal of Control, 10.1002/asjc.1985, 22, 3, 1025-1037, 2020.05, [URL]. |

4. | Hayato Waki, Positive Definiteness in Linear Matrix Inequality Problem for H-infinity Output Feedback Control Problem, IEEE Control Systems Letters, DOI:/10.1109/LCSYS.2019.2898385, 3, 2, 446-451, 2019.04, [URL]. |

5. | Hayato Waki, Noboru Sebe, Application of Facial Reduction to $H_\infty$ State Feedback Control Problem, International Journal of Control, http://dx.doi.org/10.1080/00207179.2017.1351625, 92, 2, 303-316, 2019.04, [URL]. |

6. | Hayato Waki, Noboru Sebe, Strong feasibility of the dual problem of linear matrix inequality for H-infinity output feedback control problem, Proceedings of SICE International Symposium on Control Systems 2018, 10.23919/SICEISCS.2018.8330155, 47-53, 2018.03. |

7. | Hayato Waki, Noboru Sebe, Reduction of H-infinity state feedback control problems for the servo systems, Proceedings of 2017 11th Asian Control Conference (ASCC), 10.1109/ASCC.2017.8287524, 2244-2249, 2017.12. |

8. | Hayato Waki, Florin Nae, Boundary modeling in model-based calibration for automotive engines via the vertex representation of the convex hulls, Pacific Journal of Mathematics for Industry, 10.1186/s40736-016-0027-7, 9, 1, 2017.01, [URL], 2014年度に実施したIMI短期共同研究「境界モデル手法の研究」及び, 2015年度に実施したIMI短期共同研究「数学・数理科学の視点からのエンジン適合の研究」の成果の一部に相当し, 自動車エンジンの開発過程の一つである境界モデリングに関して最適化技術を用いて効率化を実現した.. |

9. | Hayato Waki, Yoshio Ebihara, Noboru Sebe, Reduction of SDPs in H∞ control of SISO systems and performance limitations analysis, IEEE 55th Conference on Decision and Control (CDC), 2016, 10.1109/CDC.2016.7798342, 2016.12, [URL]. |

10. | Hayato Waki, Noboru Sebe, Application of Facial Reduction to $H_¥infty$ State Feedback Control Problem, The 8th IFAC Robust Control Design (ROCOND 2015), doi:10.1016/j.ifacol.2015.09.443, 48, 14, 113-119, 2015.07. |

11. | Hayato Waki, How to generate weakly infeasible semidefinite programs via Lasserre's relaxations for polynomial optimization, OPTIMIZATION LETTERS, 10.1007/s11590-011-0384-1, 6, 8, 1883-1896, 2012.12. |

12. | Hayato Waki, Nakata, Maho, Muramatsu, Masakazu, Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization, Computational Optimization and Applications, 10.1007/s10589-011-9437-8, 53, 3, 823-844, 2012.12. |

13. | Hayato Waki, Masakazu Muramatsu, Facial Reduction Algorithms for Conic Optimization Problems, Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-012-0219-y, 158, 1, 188-215, 2013.07. |

14. | Hayato Waki, Masakazu Muramatsu, An extension of the elimination method for a sparse SOS polynomial, Journal of the Operations Research Society of Japan, 54, 4, 161--190, 2011.12, [URL]. |

15. | Hayato Waki, Masakazu Muramatsu, A Facial Reduction Algorithm for Finding Sparse SOS representations, Operations Research Letters, http://dx.doi.org/10.1016/j.orl.2010.05.011, 38, 5, 361--365, 2010.09, [URL]. |

16. | Hayato Waki, Masakazu Muramatsu, Masakazu Kojima, INVARIANCE UNDER AFFINE TRANSFORMATION IN SEMIDEFINITE PROGRAMMING RELAXATION FOR POLYNOMIAL OPTIMIZATION PROBLEMS, Pacific Journal of Optimization, 5, 2, 297-312, 2009.05. |

17. | Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu, Hiroshi Sugimoto, Algorithm 883: SparsePOP -- a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems, ACM Transactions on Mathematical Software, http://doi.acm.org/10.1145/1377612.1377619, 15, 2, 15:1--15:13, 2008.07. |

18. | Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu, Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity, SIAM Journal on Optimization, http://dx.doi.org/10.1137/050623802, 17, 1, 218-242, 2006.05. |

19. | Masakazu Kojima, Sunyoung Kim, Hayato Waki, Sparsity in sums of squares of polynomials, Mathematical Programming, 10.1007/s10107-004-0554-3, 103, 1, 45-62, 2005.05. |

**Presentations**

1. | Hayato Waki, Noboru Sebe, Yoshio Ebihara, Facial reduction for H-infinity state feedback control, International Workshop on "Control and Optimization", 2018.11, [URL]. |

2. | Hayato Waki, Ill-posed semidefinite program, Joint Mini-workshop between KU and NTNU, 2018.10, [URL]. |

3. | Hayato Waki, Noboru Sebe, Strong feasibility of the dual problem of linear matrix inequality for H-infinity output feedback control problem, 2018 SICE International Symposium on Control Systems (SICE ISCS), 2018.03, [URL]. |

4. | 脇 隼人, Computational aspects on non-strictly feasible semidefinite program, PROJECT COLLOQUIA in ERATO MMSD, 2017.07, [URL]. |

5. | Hayato Waki, An Introduction on SemiDefinite Program -- from the viewpoint of computation --, Combinatorial Optimization at Work, 2015.10, [URL]. |

6. | Hayato Waki, Noboru Sebe, Application of Facial Reduction to H_¥infty State Feedback Control Problem, 22nd International Symposium on Optimization, 2015.07, [URL]. |

7. | Hayato Waki, Noboru Sebe, Application of Facial Reduction to H_¥infty State Feedback Control Problem, 8th IFAC Symposium on Robust Control Design, 2015.07, [URL]. |

8. | Hayato Waki, Masakazu Muramatsu and Levent Tuncel, A perturbed sums of squares theorem for polynomial optimization and its applications, Optimization: Computation, Theory and Modeling, 2012.11, [URL]. |

9. | , [URL]. |

10. | Hayato Waki, Masakazu Muramatsu, Computation of Facial Reduction, INFORMS Annual Meeting 2012 Phoenix, 2012.10. |

11. | Hayato Waki, Masakazu Muramatsu, Computation of facial reduction algorithm, 21st International Symposium on Mathematical Programming, 2012.08. |

12. | Hayato Waki, Maho Nakata and Masakazu Muramatsu, Strange Behaviors of Interior-Point Methods for Solving Semidefinite Programming Problems, Advanced Optimization Laboratory Seminars Series, 2011.09, [URL]. |

13. | , [URL]. |

14. | Masakazu Kojima, Kim Sunyoung, Masakazu Muramatsu, Hiroshi Sugimoto and Makoto Yamashita, SparsePOP: A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems, Informs annual meeting 2010, 2010.11, [URL]. |

15. | Hayato Waki, SDP relaxation for Polynomial Optimization Problems and Facial Reduction Algorithm, The International Conference on Continuous Optimization (ICCOPT) 2010, 2010.07, [URL]. |

16. | Hayato Waki, Strange Behaviors of Interior-Point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization, 2nd Alpen-Adria Workshop on Optimization , 2011.05. |

17. | Hayato Waki, Strange Behaviors of Interior-Point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization, SIAM Conference on Optimization 2011, 2011.05. |

**Membership in Academic Society**

- The Japan Society for Industrial and Applied Mathematics
- The Operations Research Society of Japan

Educational

**Educational Activities**

I teach calculus for the first-year student, theory of complex function for students in Dept. Eng, numerical computation for students which belong in Dept. of Math. and theory of optimization for students in graduate school.

Social

**Professional and Outreach Activities**

An agreement on academic cooperation between the institute of mathematics for industry and Zuse Institute Berlin was concluded in 2014 spring. We carried out the following three events:

(1) An international workshop ``Workshop on Optimization in the Real World" was held on Ito campus, Kyushu University, on 14--15 Oct. 2014. This workshop was organized by Professor Katsuki Fujisawa (Institute of mathematics for industry, Kyushu University), Yuji Shinano (Zuse Institute Berlin), and me. We invited Zuse Institute of Berlin of President and Professor Martine Groetschel and some researchers.

(2) Combinatorial Optimization @ Work was held in Berlin, 27 Sept. -- 9 Oct, 2015. Professor Fujisawa and I give lectures on optimization to students

(3) We published a post-proceedings on the workshop (1) as a book in the series Mathematics for Industry, Springer..

(1) An international workshop ``Workshop on Optimization in the Real World" was held on Ito campus, Kyushu University, on 14--15 Oct. 2014. This workshop was organized by Professor Katsuki Fujisawa (Institute of mathematics for industry, Kyushu University), Yuji Shinano (Zuse Institute Berlin), and me. We invited Zuse Institute of Berlin of President and Professor Martine Groetschel and some researchers.

(2) Combinatorial Optimization @ Work was held in Berlin, 27 Sept. -- 9 Oct, 2015. Professor Fujisawa and I give lectures on optimization to students

(3) We published a post-proceedings on the workshop (1) as a book in the series Mathematics for Industry, Springer..

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