A parallel implementation for solving large-scale Semidefinite Programs having sparse Schur complement matrix

• Project/Area Number: 21710148
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Social systems engineering/Safety system
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: YAMASHITA Makoto 東京工業大学, 大学院・情報理工学研究科, 助教 (20386824)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 応用数学 / ハイパフォーマンスコンピューティング / 数理最適化 / 並列計算 / 半正定値計画問題 / センサーネットワーク

Research Abstract

The reduction in computation time for solving Semidefinite Programs is essential to many applications like sensor network localization problems and polynomial optimizations. We focus on the sparsity of the Schur complement matrix, which occupies most computation time. We estimate the computation cost of each element of the matrix and propose efficient parallel schemes. From numerical results, we verified that the parallel schemes successfully reduce the computation time.

Research Products

• [Journal Article] Enclosing Ellipsoids and Elliptic Cylynders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization (2013)
  • Author(s): M. Kojima, M. Yamashita
  • Journal Title: Mathematical Programming Volume: 138(1-2) Issue: 1-2 Pages: 333-364
  • DOI: 10.1007/s10107-012-0515-1
  • Peer Reviewed
• [Journal Article] Parallel solver for semidefinite programming problem having sparse Schur complement matrix (2012)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Journal Title: ACM Transactions on Mathematical Software
  • Peer Reviewed
• [Journal Article] SFSDP : a Sparse Version of Full Semi Definite Programming Relaxation for Sensor Network Localization Problems (2012)
  • Author(s): Sunyoung Kim, Masakazu Kojima, Hayato Waki, Makoto Yamashita
  • Journal Title: ACM Transactions on Mathematical Software
  • Peer Reviewed
• [Journal Article] Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization (2012)
  • Author(s): Masakazu Kojima, Makoto Yamashita
  • Journal Title: Mathematical Programming
  • Peer Reviewed
• [Journal Article] SFSDP : a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems (2012)
  • Author(s): Sunyoung Kim, Masakazu Kojima, Hayato Waki, Makoto Yamashita
  • Journal Title: ACM Transactions on Mathematical Software Volume: (掲載決定)(DOI未定)
  • Peer Reviewed
• [Journal Article] High Performance Solvers for Semidefinite Programs (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Kazuhiro Kobayashi, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Journal Title: Proceedings of the Korean Society for Industrial and Appplied Mathematcis Volume: Vol.6, No.2 Pages: 55-58
• [Journal Article] Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion (2011)
  • Author(s): Sunyoung Kim, Masakazu Kojima, Martin Mevissen, Makoto Yamashita
  • Journal Title: Mathematical Programming Volume: Vol.129, No.1 Pages: 33-68
  • Peer Reviewed
• [Journal Article] Constructing Polyhedral Homotopies on Grid-of-Clusters (2011)
  • Author(s): Tomohiko Mizutani, Makoto Yamashita
  • Journal Title: Pacific Journal on Optimization Volume: Vol.7, No.2 Pages: 369-386
• [Journal Article] High Performance Solvers for Semidefinite Programs (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Journal Title: Proceedings of the Korean Society for Industrial and Appplied Mathematcis Volume: Vol6 No2 Pages: 56-58
• [Journal Article] Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion (2011)
  • Author(s): Sunyoung Kim, Masakazu Kojima, Martin Mevissen, Makoto Yamashita
  • Journal Title: Mathematical Programming Series B Volume: Vol129 No1 Issue: 1 Pages: 33-68
  • DOI: 10.1007/s10107-010-0402-6
  • Peer Reviewed
• [Journal Article] Efficient Parallel Software for Large-Scale Semidefinite Programs (2010)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa
  • Journal Title: Proceedings of 2010 IEEE International Symposium on Computer-Aided Control System Design Pages: 178-178
  • Peer Reviewed
• [Journal Article] 主双対内点法に対する高速化・並列化の技術 (2010)
  • Author(s): 山下真
  • Journal Title: オペレーションズ・リサーチ Volume: 55(7) Pages: 400-405
  • NAID: 110007657899
  • Peer Reviewed
• [Presentation] High Performance Solvers for Semidefinite Programs (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
  • Organizer: KSIAM Annual Meeting 2011
  • Place of Presentation: Seogwipo, South Korea
  • Year and Date: 2011-11-25
• [Presentation] High Performance Solvers for Semidefinite Programs (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Organizer: KSIAM Annual Meeting 2011
  • Place of Presentation: Seogwipo KAL Hotel(韓国)
  • Year and Date: 2011-11-25
• [Presentation] Parallel Computation for SDPs Focusing on the Sparsity of Schur Complements Matrices (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Organizer: INFORMS Annual Meeting 2011
  • Place of Presentation: Charlotte, USA
  • Year and Date: 2011-11-15
• [Presentation] Parallel Computation for SDPs Focusing on the Sparsity of Schur Complements Matrices (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
  • Organizer: INFORMS Annual Meeting 2011
  • Place of Presentation: Charlotte Conference Center(アメリカ)
  • Year and Date: 2011-11-15
• [Presentation] Ellipsoid-type Confidential Bounds on Semi-algebraic Sets via SDP Relaxation (2011)
  • Author(s): Makoto Yamashita and Masakazu Kojima
  • Organizer: SIAM Conference on Optimization 2011
  • Place of Presentation: Darmstadt, Germany
  • Year and Date: 2011-05-18
• [Presentation] Ellipsoid-type Confidential Bounds on Semi-algebraic Sets via SDP Relaxation (2011)
  • Author(s): Makoto Yamashita, Masakazu Kojima
  • Organizer: Siam Conference on Optimization 2011
  • Place of Presentation: Darmstadtium Conference Center(ドイツ)
  • Year and Date: 2011-05-18
• [Presentation] SDPARA : a parallel software for large-scale SDP based on primal-dual interior-point methods (2010)
  • Author(s): Makoto Yamashita
  • Organizer: Parallel Computing and SDP Workshop
  • Place of Presentation: Berlin, Germany
  • Year and Date: 2010-12-01
• [Presentation] SDPARA : a parallel software for large-scale SDP based on primal-dual interior-point methods (2010)
  • Author(s): Makoto Yamashita
  • Organizer: Parallel Computing and SDP Workshop
  • Place of Presentation: Zuse-Institut Berlin (Berlin, Germany)
  • Year and Date: 2010-12-01
• [Presentation] Efficient Parallel Software for Large-Scale Semidefinite Programs (2010)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa
  • Organizer: 2010 IEEE Multi-Conference on Systems and Control
  • Place of Presentation: 横浜,日本
  • Year and Date: 2010-09-08
• [Presentation] Efficient Parallel Software for Large-Scale Semidefinite Programs (2010)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa
  • Organizer: 2010 IEEE Multi-Conference on Systems and Control
  • Place of Presentation: パシフィコ横浜(横浜,日本)
  • Year and Date: 2010-09-08
• [Presentation] Enclosing Ellipsoids of Semi-algebraic Sets and Error Bounds in Polynomial Optimization (2010)
  • Author(s): Makoto Yamashita, Masakazu Kojima
  • Organizer: Nonlinear Optimization, Variational Inequalities and Equilibrium Problems
  • Place of Presentation: Erice, Italy
  • Year and Date: 2010-07-05
• [Presentation] Enclosing Ellipsoids of Semi-algebraic Sets and Error Bounds in Polynomial Optimization (2010)
  • Author(s): Makoto Yamashita, Masakazu Kojima
  • Organizer: Nonlinear Optimization, Variational Inequalities and Equilibrium Problems
  • Place of Presentation: "E.Majorana" Centre for Scientific Culture (Erice, Italy)
  • Year and Date: 2010-07-05
• [Presentation] Parallel Software for Semi Definite Programming with Sparse Schur Complement Matrix (2009)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Yoshiaki Futakata, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
  • Organizer: The International Symposium on Mathematical Programming 2009
  • Place of Presentation: Chicago, USA
  • Year and Date: 2009-08-26
• [Presentation] Parallel Software for SemiDefinite Programming with Sparse Schur Complmenent Matrix (2009)
  • Author(s): Makoto Yamashita
  • Organizer: The International Symposium on Mathematical Programming 2009
  • Place of Presentation: Chicago, USA
  • Year and Date: 2009-08-26
• [Book] Latest developments in the SDPA Family for solving large-scale SDPs,inHandbook on Semidefinite, Cone and Polynomial Optimization : Theory, Algorithms, Software and Applicationsedited by Miguel F. Anjos and Jean B. Lasserre (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakta, Maho Nakata
  • Publisher: Springer, NY, USA
• [Book] Latest developments in the SDPA Family for solving large-scale SDPs in "Handbook on Semidefinite, Cone and Polynomial Optimization : Theory, Algorithms, Software and Applications" edited by Miguel F.Anjos and Jean B.Lasserre (2011)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakta, Maho Nakata
  • Total Pages: 28
  • Publisher: Springer
• [Remarks] 半正定値計画問題ソフトウェアSDPAおよびSDPARAのホームページ
  • URL: http://sdpa.sourceforge.net/
• [Remarks]
  • URL: http://sdpa.sourceforge.net/
• [Remarks] SDPA,SDPARAのホームページ
  • URL: http://sdpa.sourceforge.net/
• [Remarks] 富士通によるプレスリリース
  • URL: http://pr.fujitsu.com/jp/news/2010/05/28.html
• [Remarks]
  • URL: http://sdpa.indsys.chuo-u.ac.jp/sdpa/