(At mount Palnock 2011, May 14)

Institute of Mathematics for Industry, Kyushu University

Position: Associate Professor

waki (AT) imi.kyushu-u.ac.jp

or

hayato.waki (AT) gmail.com

Caution: Don’t attach tar, tar.gz, gz and exe files.

Research: Optimization

 I am interested in the use of SemiDefinite programming (SDP) problem for optimization problems described with polynomials. We call the optimization problem Polynomial Optimization Problem (POP). Finding the global optimal solution and value of POP is well-known as NP-hard.

 The following site has our developed software which finds the global optimal value or the lower bound for POP: SparsePOP

My Citations by Google Scholar

Talk

Paper

• 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)

• 脇隼人, 村松正和,  ``ジョルダン代数'', オペレーションズ・リサーチ誌, Vol. 55 (11) 718(48) - 719(49) (2010), (in Japanese)

• 脇隼人, 村松正和,  ``二次錐計画'', オペレーションズ・リサーチ誌, Vol. 55 (10) 655(47) - 656(48) (2010), (in Japanese)

.• H. Waki and M. Muramatsu, "A Facial Reduction Algorithm for Finding Sparse SOS representations", Operations Research Letters, Volume 38, Issue 5, 361--365 (2010)

 • H. Waki and M. Muramatsu, "Facial Reduction Algorithms for Conic Optimization Problems", Technical Report CS-09-01,  Dept. of Comp. Science, The University of Electro-Communications, available from optimization-online

• 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)

• Y. Sekiguchi, T. Takenawa and H. Waki, "Real ideal and the duality of semidefinite programming for polynomial optimizaiton", available from arXiv.org

• H. Waki, M. Nakata and M. Muramatsu, "Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization", To appear in Computational Optimization and Applications, DOI: 10.1007/s10589-011-9437-8 Related site

• 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.

• 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)

• 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)

• 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).

• 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).

• 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).

• M. Kojima, S. Kim and H. Waki, "Sparsity in Sums of Squares of Polynomials'', Mathematical Programming, Vol.103 (1) 45-62 (2005). 

• 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), (in Japanease).

• 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).

Class 

Education

• 2002. Mar... B.Sc.,  Dept. of Information Science, Tokyo Institute of Technology. 

• 2004. Mar... M.Sc., Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology.

• 2007. Mar... Ph.D., Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology.

“Semidefinite Programming and Sums of Squares Relaxations for Sparse Polynomial Optimization Problems” Supervisor: Professor Masakazu Kojima