Publications

Papers with refereed

  1. Y. Ebihara, H. Waki, V. Magron, N. H. A. Mai, D. Peaucelle, and S. Tarbouriech, “ l2 Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks,” The 2021 ECC Special Issue of the European Journal of Control, to appear (2021) doi.org/10.1016/j.ejcon.2021.06.022

  2. Y. Sekiguchi and H. Waki, ``Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems", Journal of Optimization Theory and Applications, (2020) doi.org/10.1007/s10957-020-01780-0

  3. H. Waki and N. 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, (2020) DOI:0.1007/s00498-020-00261-z

  4. Y. Ebihara, N. Sebe and H. Waki, ``On Gain-Scheduled State-Feedback Controller Synthesis With Quadratic Stability Condition", IEEE Control Systems Letters, Vol.4 (3), 662-667 (2020) DOI:10.1109/LCSYS.2020.2991480

  5. H. Waki, ``Positive Definiteness in Linear Matrix Inequality Problem for H-infinity Output Feedback Control", IEEE Control Systems Letters, Vol.3 (2), 446--451 (2019) DOI:10.1109/LCSYS.2019.2898385

  6. H. Waki and N. Sebe, ``Reduction of H_infty state feedback control problems for the servo systems", Asian Journal of Control, Vol. 22 (3), 1025--1037 (2020) DOI:10.1002/asjc.1985. 4th Kimura Best Paper Award

  7. K. Kimura, H. Waki and M. Yasuda, ``Application of mixed integer quadratic program to shortest vector problems", JSIAM Letters, Vol.9, 65--68 (2017) site

  8. H. Waki and N. Sebe, "Application of Facial Reduction to H_infty State Feedback Control Problem", International Journal of Control, Vol. 92 (2), 303--316 (2019) DOI:10.1080/00207179.2017.1351625

  9. K. Kimura and H. Waki, "Minimization of Akaike's Information Criterion in Linear Regression Analysis via Mixed Integer Nonlinear Program", Optimization Methods and Software, Vol. 33 (3), 633--649 (2018) DOI:10.1080/10556788.2017.1333611

  10. H. Waki and F. Nae, "Boundary modeling-based calibration for automotive engines via the vertex representation of the convex hulls", Pacific Journal of Mathematics for Industry, 9:1, (2017) DOI: 10.1186/s40736-016-0027-7

  11. M. Muramatsu, H. Waki and L. Tuncel, "A Perturbed Sums of Squares Theorem for Polynomial Optimization and its Applications", Optimization Methods and Software, Vol. 31 (1), 134--156 (2016) DOI: 10.1080/10556788.2015.1052969

  12. M. Tanaka, N. Nakata and H. Waki, "Numerical reduction method for doubly nonnegative optimization problems", Journal of Math-for-Industry, Vol. 5 A 41--50 (2013) available from here

  13. T. Osogami, T. Shirai and H. Waki, "Remarks on positivity of alpha-determinants via SDP relaxation", Journal of Math-for-Industry, Vol. 5 A 1--10 (2013) available from here

  14. M. Tanaka, N. Nakata and H. Waki, "Application of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative relaxation for mixed binary nonconvex quadratic optimization problems", Pacific Journal of Optimization, Vol. 8 699--724 (2012) available from here

  15. H. Waki, "How to generate weakly infeasible semidefinite programs via Lasserre's relaxations for polynomial optimization", Optimization Letters, Vol. 6 (8), 1883-1896 (2012) DOI: 10.1007/s11590-011-0384-1 Related site

  16. H. Waki and M. Muramatsu, "An extension of the elimination method for a sparse SOS polynomial", Journal of the Operations Research Society of Japan, Vol. 54 (4), 161--190 (2011) available from here

  17. H. Waki and M. Muramatsu, "A Facial Reduction Algorithm for Finding Sparse SOS representations", Operations Research Letters, Vol. 38 (5), 361--365 (2010) DOI: 10.1016/j.orl.2010.05.011

  18. H. Waki and M. Muramatsu, "Facial Reduction Algorithms for Conic Optimization Problems", Journal of Optimization Theory and Applications, Vol. 158 (1), 188--215 DOI: 10.1007/s10957-012-0219-y

  19. S. Kim, M. Kojima, H. Waki and M. Yamashita, "SFSDP: a Sparse version of Full SemiDefinite Programming relaxation for sensor network localization problems", Transactions on Mathematical Software, Vol. 38 (4), (2011) DOI: 10.1145/2331130.2331135

  20. Y. Sekiguchi, T. Takenawa and H. Waki, "Real ideal and the duality of semidefinite programming for polynomial optimization", Japan Journal of Industrial and Applied Mathematics, Vol. 30, 321--330 (2013) DOI 10.1007/s13160.013-0104-6

  21. H. Waki, M. Nakata and M. Muramatsu, "Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization", Computational Optimization and Applications, Vol. 53 (3), 823--844 (2012) DOI: 10.1007/s10589-011-9437-8 Related site

  22. S. Kim, M. Kojima. and H. Waki, "Exploiting Sparsity in SDP Relaxation for Sensor Network Localization", SIAM Journal on Optimization, Vol.20 (1), 192--215 (2009) DOI: 10.1137/080713380

  23. H. Waki, M. Muramatsu and M. Kojima, "Invariance under Affine Transformation in Semidefinite Programming Relaxation for Polynomial Optimization Problems", Pacific Journal of Optimization, Vol. 5 (2), 297--312 (2009) available from here

  24. H. Waki, S. Kim, M. Kojima, M. Muramatsu and H. Sugimoto, "SparsePOP : a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems", ACM Transactions on Mathematical Software, Vol. 15 (2), 15 (2008) DOI: 10.1145/1377612.1377619

  25. H. Waki, S. Kim, M. Kojima and M. Muramatsu, "Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity", SIAM Journal on Optimization, Vol.17 (1), 218-242 (2006) DOI: 10.1137/050623802

  26. S. Kim, M. Kojima and H. Waki, "Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems", SIAM Journal on Optimization, Vol. 15 (3), 697-719 (2005) DOI: 10.1137/030601260

  27. M. Kojima, S. Kim and H. Waki, "Sparsity in Sums of Squares of Polynomials'', Mathematical Programming, Vol.103 (1), 45-62 (2005) DOI: 10.1007/s10107-004-0554-3

  28. M. Kojima, S. Kim and H. Waki, "A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones'', Journal of Operations Research Society of Japan, Vol. 46 (2), 125-144 (2003), available from here

Papers in refereed conferences

  1. H. Waki and N. 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, DOI: 10.23919/SICESCS.2018.8330155

  2. H. Waki and N. Sebe, ``Reduction of H_infty state feedback control problems for the servo systems", Proceedings of 2017 11th Asian Control Conference (ASCC), 2244--2249, 2017 DOI: 10.1109/ASCC.2017.8287524

  3. H. Waki, Y. Ebihara and N. Sebe, "Reduction of SDPs in H∞ control of SISO systems and performance limitations analysis", Proceedings of 55th IEEE Conference on Decision and Control, Las Vegas, USA, December 12-14, 2016 DOI: 10.1109/CDC.2016.7798342

  4. Y. Ebihara, H. Waki and N. Sebe, "Dual LMI approach to H∞ performance limitation analysis of sensitivity and complementary sensitivity functions", Proceedings of Computer Aided Control System Design (CACSD), 2016 DOI: 10.1109/CACSD.2016.7602558

  5. K. Kimura and H. Waki, "Mixed Integer Nonlinear Program for Minimization of Akaike's Information Criterion", the Proceedings of the 5th International Congress on Mathematical Software, Berlin, Germany, July 11-14, 2016 DOI: 10.1007/978-3-319-42432-3_36

  6. Y. Ebihara, H. Waki and N. Sebe, "H-Infinity Performance Limitations Analysis for SISO Systems: A Dual LMI Approach", Proceedings of 54th IEEE Conference on Decision and Control, Osaka, Japan, December 15-18, 2015 DOI: 10.1109/CDC.2015.7403263

  7. H. Waki and N. Sebe, "Application of Facial Reduction to H_¥infty State Feedback Control Problem", Proceedings of The 8th IFAC Robust Control Design 2015 (ROCOND 2015), 112-118, Bratislava, Slovakia, July, 2015 DOI: 10.1016/j.ifacol.2015.09.443

  8. K. Fujisawa, T. Endo, Y. Yasui, H. Sato, N. Matsuzawa, S. Matsuoka and H. Waki, "Peta-scale General Solver for Semidefinite Programming Problems with over Two Million Constraints", Proceedings of the International Conference on Parallel and Distributed Processing Symposium 2014 (IPDPS2014), 1171-1180, Phoenix, USA, May, 2014 DOI: 10.1109/IPDPS.2014.121

Chapters in book

  1. F. Nae and H. Waki, ``Vertex Representation of Convex Hulls for Fast Evaluation of Boundary Constraints in Model-Based Calibration for Automotive Engines", to appear in Proceedings of Forum ``Math-for-Industry" 2016, Springer, 2017.

  2. K. Kimura and H. Waki, ``A Mixed Integer Quadratic Formulation for the Shortest Vector Problem", to appear in ``Mathematical Modeling for Next-Generation Cryptography: CREST Crypto-Math Project (T. Takagi et al. eds.)", Springer, 239--255, 2018 DOI: 10.1007/978-981-10-5065-7_13

  3. H. Waki, "Strict Feasibility of Conic Optimization Problems", In Series: Mathematics for Industry "A Mathematical Approach to Research Problems of Science and Technology" (Nishii et al eds.), Vol. 5, 325--335, 2014 DOI: 10.1007/978-4-431-55060-0_24

Edited book

  1. K. Fujisawa, Y. Shimano and H. Waki, "Optimization in the Real World", In Series: Mathematics for Industry, Vol. 13, Springer, 2016 DOI:10.1007/978-4-431-55420-2

Preprint

  1. S. Kim, M. Kojima and H.Waki, "User Manual for SFSDP: a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems", Research Report B-449 (pdf), Dept. of Math. and Comp. Science, Tokyo Institute of Technology.

日本語による解説記事等

  1. 蛯原義雄, 脇隼人, 瀬部昇, ``半正定値計画によるH∞性能限界解析", 計測と制御, 59, 218--225, 2020, 記事.

  2. 脇隼人, 村松正和, "ジョルダン代数", オペレーションズリサーチ, Vol. 55, 11, 718--719, 2010, 記事.

  3. 脇隼人, 村松正和, "二次錐計画", オペレーションズリサーチ, Vol. 55, 10, 657--658, 2010, 記事.

  4. 脇隼人, "多項式最適化問題に対する半正定値計画緩和", オペレーションズリサーチ, Vol. 55, 7, 412--417, 2010, 記事.

  5. 小島政和, 脇隼人, "多項式最適化問題に対する半正定値計画緩和", システム/制御/情報, Vol. 48, 12, 477--482, 2004, 記事.