-->|第１ページ |発表論文 |著書，和文解説記事 |

B-486: N. Ito, S. Kim, M. Kojima, A. Takeda and K. Toh, " Equivalences and Differences in Conic Relaxations of Combinatorial Quadratic Optimization Problems", July 2017. pdf file.

B-483: S. Kim, M. Kojima and K. Toh, "Doubly Nonnegative Relaxations for Quadratic and Polynomial Optimization Problems with Binary and Box Constraints", July 2016. pdf file.

B-482: N. Arima, S. Kim, M. Kojima and K. Toh, "A Robust Lagrangian-DNN Method for a Class of Quadratic Optimization Problems", February 2016. pdf file.

B-481: S. Kim and M. Kojima, "Binary Quadratic Optimization Problems That Are Difficult to Solve by Conic Relaxations", July 2015. pdf file.

B-476: N. Arima, S. Kim, M. Kojima and K. Toh, "Lagrangian-Conic Relaxations, Part II: Applications to Polynomial Optimization Problems", January 2014. pdf file.

B-475: N. Arima, S. Kim, M. Kojima and K. Toh, "Lagrangian-Conic Relaxations, Part I: A Unified Framework and Its Applications to Quadratic Optimization Problems ", January 2014. pdf file.

B-472: S. Kim, M. Kojima and K. Toh, "A Lagrangian-DNN Relaxation: a Fast Method for Computing Tight Lower Bounds for a Class of Quadratic Optimization Problems ", October 2013. pdf file.

2013-4: S. Burer, S.Kim and M. Kojima, "Faster, but Weaker, Relaxations for Quadratically Constrained Quadratic Programs ", April, 2013, pdf file.

B-471: N. Arima, S. Kim and M. Kojima, "Extension of Completely Positive Cone Relaxation to Polynomial Optimization ", February 2013. pdf file.

B-470: S. Kim, M. Kojima and M. Yamashita, "Parallel Implementation of Successive Sparse SDP Relaxations for Large-Scale Euclidean Distance Geometry Problems ", November 2012. pdf file.

B-469: N. Arima, S. Kim and M. Kojima, "Simplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables ", October 2012. pdf file.

B-468: N. Arima, S. Kim and M. Kojima, "A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming ", September 2012. pdf file.

B-466: S. Kim and M. Kojima, "A Continuation Method for Large-sized Sensor Network Localization Problems", August 2011. pdf file.

B-462: S. Kim and M. Kojima, "Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems", May 2010. pdf file.

B-459: M. Kojima and M. Yamashita, "Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization", November 2009. pdf file.

B-457: S. Kim, M. Kojima H. Waki and M. Yamashita, "SFSDP: a Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems ", July 2009. pdf file.

B-455: M. Mevissen and M. Kojima, "SDP Relaxations for Quadratic Optimization
Problems Derived from Polynomial Optimization Problems", April 2009. *Asia-Pacific Journal of Operational Research* Vol 27 (1) 15-38 (2010).

B-453: K. Fujisawa, S. Kim, M. Kojima, Y. Okamoto and M. Yamashita, "User's Manual for SparseCoLO: Conversion Methods for SPARSE COnic-form Linear Optimization Problems", February 2009. pdf file. MATLAB Software Package SparseCoLO.

B-452: S. Kim, M. Kojima, M. Mevissen and M. Yamashita, "Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion", January 2009. pdf file. To appear in *Mathematical Programming. *

B-449: S. Kim, M. Kojima and H. Waki, "User manual for SFSDP: a Sparse Version of Full SemiDefinite Programming relaxation for sensor network localization problem", August 2008. pdf file. MATLAB software package SFSDP.

B-448: Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Masakazu Kojima, Kazuhide Nakata, Maho Nakata and Makoto Yamashita, "SDPA (SemiDefinite Programming Algorithm) User's Manual --- Version 7.0.5", February 2008. pdf file.

B-447: S. Kim, M. Kojima and H. Waki, "Exploiting Sparsity in SDP Relaxation
for Sensor Network Localization", January 2008. Revised October 2008. *SIAM Journal of Optimization* Vol.20 (1) 192-215 (2009). MATLAB software package SFSDP.

B-445: K. Murota, Y. Kanno, M. Kojima and S. Kojima, " A numerical algorithm for block-diagonal decomposition of matrix *-algebras, Part I: proposed approach and application to semidefinite programming", *Japan Journal of Industrial and Applied Mathematics* Vol.27 125-160 (2010).

B-444: S. Kim and M. Kojima, "Solving polynomial least squares problems
via semidefinite programming relaxations", *Journal
of Global Optimization* VOL.46 (1) 1-23 (2010).

B-442: M. Mevissen, M. Kojima, J. Nie and N. Takayama, "Solving partial
differential equations via sparse SDP relaxations",*Pacific Journal
of Optimization* Vol. 4 (2) 213 - 241 (2008). pdf
file.

B-440: K. Kobayashi, S, Kim and M. Kojima, "Sparse Second Order Cone Programming
Formulations for Convex Optimization Problems", March 2007. *Journal
of the Operations Research Society of Japan* Vol 51 (3) 241-264 (2008).
pdf file.

B-438: K. Suzuki, N. Miyoshi and M. Kojima, " 拡散過程の生存確率に対する半正定値計画を用いた数値計算手法
", January 2007. *Transactions of the Operations Research Society of
Japan* Vol.51 25-43 (2008). pdf file.

B-437: C. Vo, M. Muramatsu and M. Kojima, " Equality Based Contraction
of Semidefinite Programming Relaxations in Polynomial Optimization ", December
2006. *Journal of the Operations Research Society of Japan* Vol. 51 (1) 111-125 (2008).

B-435: H. Waki, M. Muramatsu and M. Kojima, "Invariance under Affine Transformation
in Semidefinite Programming Relaxation for Polynomial Optimization Problems
", October 2006. *Pacific Journal of Optimization* Vol 5 (2) 297-312 (2009). pdf file.

B-434: K. Kobayashi, S. Kim and M. Kojima, "Correlative Sparsity in Primal-Dual
Interior-Point Methods for LP, SDP and SOCP", *Applied Mathematics and Optimization* Vol 58 (1) 69-88 pdf
file.

B-433: M. Kojima, "Efficient Evaluation of Polynomials and Their Partial
Derivatives in Homotopy Continuation Methods", August 2006. Revised July
2007. *Journal of the Operations Research Society of Japan* Vol. 51 (1) 29-54 (2008).

B-428: S. Kim, M. Kojima and Ph.~L.~Toint, " Recognizing Underlying Sparsity
in Optimization ", May 2006.* Mathematical Programming* Vol19 (2) 273-303 (2009). pdf file.

B-422: T. Mizutani, A. Takeda and M. Kojima, " Dynamic Enumeration of
All Mixed Cells ", *Discrete and Computational Geometry* Vol. 37
(3) 351-367 (2007).

B-421: M. Kojima and M. Muramatsu, " A Note on Sparse SOS and SDP Relaxations
for Polynomial Optimization Problems over Symmetric Cones ", Janurary 2006.
Revised February 2007. *Computational Optimization and Applications*
Vol 42 (1) 31-41 (2009). pdf file.

B-419: T. Gunji, S. Kim, K. Fujisawa and M. Kojima, "PHoMpara -- Parallel
Implementation of the __P__olyhedral __Ho__motopy Continuation __M__ethod
". October 2005. Revised April 2006.*Computing* Vol. 77 (4) 387-411
(2006). pdf
file.

B-416: K. Kobayashi, K. Nakata and M. Kojima, "A Conversion of an SDP
Having Free Variables into the Standard Form SDP" June 2005. Revised April
2006, *Computational Optimization and Applications* Vol. 36 289-307 (2007).

B-415: M. Yamashita, K. Fujisawa, M. Fukuda, M. Kojima and K. Nakata, "Parallel Primal-dual Interior-Point Methods for SemiDefinite Programs", March 2005. pdf file.

B-414: H. Waki, S. Kim, M. Kojima and M. Muramatsu, "SparsePOP : a Sparse
Semidefinite Programming Relaxation of Polynomial Optimization Problems",
March 2005. Revised August 2007. *ACM Transactions on Mathematical Software*
Vol 35 (2) 15 (2008).

B-411: H. Waki, S. Kim, M. Kojima and M. Muramatsu, "Sums of Squares and
Semidefinite Programming Relaxations for Polynomial Optimization Problems with
Structured Sparsity", October 2004. Revised September 2005. *SIAM Journal
on Optimization* Vol.17 (1) 218-242 (2006).

B-409: K. Fujisawa, M. Fukuda, M. Kojima, K. Nakata and M. Yamashita, "SDPA-C (SemiDefinite Programming Algorithm -- Completion method) User's Manual --- Version 6.10", August 2004. ps file, ps.gz file, pdf file.

B-406: M. Kojima and M. Muramatsu, "An Extension of Sums of Squares Relaxations
to Polynomial Optimization Problems over Symmetric Cones ", April 2004.
Revised April 2006, *Mathematical Programming* Vol. 110 (2) 315-336 (2007).

B-405: C. Vo, A. Takeda and M. Kojima, "A Multilevel Parallelized Brancd and
Bound Hybrid Algorithm for Quadratic Optimization", March 2004. * IPSJ Transactions
on Advanced Computing Systems* Vol.45, No.SIG 6(ACS 6) 186-196 (2004).

B-400:K. Fujisawa, M. Kojima, A. Takeda and M. Yamashita, "Solving Large Scale
Optimization Problems via Grid and Cluster Computing", December 2003, *Journal
of Operations Research Society of Japan* Vol.47 (4) 265-274 (2004).

B-399: H.Waki, M.Kojima, S.Kim, "Linearization and Lagrangian Relaxation Techniques for Polynomial Programs" (in Japanese), December 2003. ps file, ps.gz file, pdf file.

B-398: K.Nakata, M.Yamashita, K.Fujisawa, M.Kojima, "A Parallel Primal-Dual
Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix
Completion", November 2003. Revised July 2005. *Parallel Computing*
Vol.32 24-43 (2006). pdf file.

B-397: M. Kojima, "Sums of Squares Relaxations of Polynomial Semidefinite Programs", November 2003. ps file, ps.gz file, pdf file.

B-396: K. Fujisawa, M. Kojima, A. Takeda and M. Yamashita, "High Performance Grid and Cluster Computing for Some Optimization Problems", October 2003. ps file, ps.gz file, pdf file. Proceedings of SAINT 2004 Workshops, 612-615 (Tokyo, Japan, Jan. 26-30, 2004).

B-395: S. Kim, M. Kojima and H. Waki, ``Generalized Lagrangian Duals and Sums
of Squares Relaxations of Sparse Polynomial Optimization Problems'', September
2003. Revised July 2004. To appear in *SIAM Journal on Optimization. *
pdf file

B-391: M. Kojima, S. Kim and H. Waki, ``Sparsity in Sums of Squares of Polynomials'',
June 2003, Revised June 2004. *Mathematical Programming* Vol.103 (1)
45-62.

B-390: S. Kim and M. Kojima, ``Numerical Stability of Path Tracing in Polyhedral
Homotopy Continuation Methods'', March 2003. Revised February 2004.*Computing*
Vol. 73 (4) 329-348 (2004).

B-386: T. Gunji, S. Kim, M. Kojima, A. Takeda, K. Fujisawa and T. Mizutani,
``PHoM -- a __P__olyhedral __Ho__motopy Continuation __M__ethod",
December 2002, revised Janurary 2003. *Computing *Vol.73 55-77 (2004).
ps file, ps.gz
file, pdf file.

B-384: M. Yamashita, K. Fujisawa and M. Kojima, ``SDPARA : __S__emi__D__efinite__
P__rogramming __A__lgorithm PA__RA__llel Version'', October 2002. *Parallel
Computing *Vol.29 (8) 1053-1067 (2003).* *ps
file, ps.gz file, pdf
file.

B-383: M. Yamashita, K. Fujisawa and M. Kojima, ``Implementation and Evaluation
of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0)'', September 2002, *Optimization
Methods and Software *Vol.18 (4) 491-505 (2003).

B-381: S. Kim, M. Kojima and M. Yamashita, ``Second Order Cone Programming
Relaxation of a Positive Semidefinite Constraint'', July 2002. *Optimization
Methods and Software * Vol.18 (5) 535-541 (2003). ps
file, ps.gz file, pdf
file.

B-380: M. Kojima, S. Kim and H. Waki, ``A General Framework for Convex Relaxation
of Polynomial Optimization Problems over Cones'', April 2002. Revised June 2002.
*Journal of Operations Research Society of Japan* Vol.46 (2) 125-144 (2003).

B-378: S. Kim and M. Kojima, ``CMPSc : A Continuation Method for Polynomial Systems (C++ version)'' ps file, ps.gz file, pdf file, March 2002. Revised April 2002. Gzipped tarred files of the entire CMPSc system.

B-376: S. Kim and M. Kojima, ``CMPSm : A Continuation Method for Polynomial
Systems (MATLAB version)'', January 2002. Revised April 2002. *Mathematical
Software, ICMS2002 Beijing, China, August 17-19 *(Arjeh M Cohen, Xiao-Shan
Gao and Nobuki Takakayama, Editors), World Scientific, Singapore, 2002. Gzipped
tarred files of the entire CMPSm system.

B-375: S. Kim and M. Kojima, ``Exact Solutions of Some Nonconvex Quadratic
Optimization Problems via SDP and SOCP Relaxations,'' January 2002. . Revised
February 2003. *Computational Optimization and Applications *Vol.26 (2)
143-154 (2003).

B-373: Y. Dai, S. Kim and M. Kojima, ``Computing All Nonsingular Solutions
of Cyclic-n Polynomial Using Polyhedral Homotopy Continuation Methods'', September
2001. Revised May 2002. *Journal of Computational and Applied Mathematics
* Vol.152, No.1-2, 83-97 (2003). Solution
Information on Some Polynomial Systems.

B-370: A. Takeda, K. Fujisawa, Y. Fukaya and M. Kojima, ``Parallel Implementation
of Successive Convex Relaxation Methods for Quadratic Optimization Problems'',
*Journal of Global Optimization*, Vol.24, No.2, 237-260.

B-369: M. Fukuda, M. Kojima and M. Shida, ``Lagrangian Dual Interior-Point
Methods for Semidefinite Programs'' , March 2001. Revised October 2001. *SIAM
Journal on Optimization *Vol 12, No.4, 1007-1031 (2002)*.*

B-368: K. Nakata, K. Fujisawa, M. Fukuda, M. Kojima and K. Murota, ``Exploiting
Sparsity in Semidefinite Programming via Matrix Completion II: Implementation
and Numerical Results'', *Mathematical Programming* Vol.95 303-327 (2003).

B-365: M. Fukuda and M. Kojima, ``Interior-Point Methods for Lagrangian Duals of Semidefinite Programs'' , December 2000.

B-364: A. Takeda, M. Kojima and K. Fujisawa, ``Enumeration of All Solutions
of a Combinatorial Linear Inequality System Arising from the Polyhedral Homotopy
Continuation Method'' , *
Journal of the Operations Research Society of Japan* Vol.45, No.1, 64-82
(2002).

B-363: S. Kim and M. Kojima, ``Second Order Cone Programming Relaxation of
Nonconvex Quadratic Optimization Problems'' ,
*Optimization Methods and Software* Vol .15, No.3-4 , 201-224 (2001).

B-359: K. Fujisawa, Y. Futakata, M. Kojima, S. Matsuyama, S. Nakamura, K. Nakata and M. Yamashita, ``SDPA-M (SemiDefinite Programming Algorithm in MATLAB) User's Manual Version 2.00'' , January 2000. Revised June 2003

B-358: M. Fukuda, M. Kojima, K. Murota and K. Nakata, ``Exploiting Sparsity
in Semidefinite Programming via Matrix Completion I: General Framework'' ,
December 1999. Revised May 2000. To appear in *SIAM Journal on Optimization
*Vol 11, No.3, 647-674 (2001).

B-356: M. Kojima and L. Tuncel, ``Some Fundamental Properties of Successive
Convex Relaxation Methods on LCP and Related Problems'', October 1999. Revised
May 2001, *Journal of Global Optimization* Vol.24, 333-348 (2002).

B-354: M. Kojima and L. Tuncel, ``On the Finite Convergence of Successive SDP
Relaxation Methods'' , August 1999. Revised August 2001. *European Journal
of Operations Research* Vol.143, No.2, 325-341 (2002).

B-352: A. Takeda and M. Kojima, ``Successive Convex Relaxation Apporach to Bilevel Quadratic Optimization Problems'' , August 1999. Applications and Algorithms of Complementarity (M. C. Ferris, O. L. Mangasarian and J.-S. Pang, Editors), Kluwer Academic Publishers, 2000, pp.317-340.

B-351: M. Fukuda and M. Kojima, ``Branch-and-Cut Algorithms for the Bilinear
Matrix Inequality Eignevalue Problem'' , April
1999. Revised January 2000. *Computational Optimization and Applications *Vol.19,
No.1, 79-105 (2001).

B-350: M. Kojima and A. Takeda, ``Complexity
Analysis of Conceptual Successive Convex Relaxation Methods for Nonconvex Sets''
, April 1999. Revised July 2000. To applear in *Mathematics of Operations
Research*.

B-349: 小島政和, ``数理計画法概論 -- 内点法を中心にして --'' , 1999年3月.

B-348: M. Kojima, T. Matsumoto, and M. Shida ``Moderate Nonconvexity = Convexity + Quadratic Concavity'' , March 1999, Revised April 1999.

B-347: A.Takeda, Y. Dai, M. Fukuda, and M. Kojima, ``Towards Implemenations
of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization
Problems'' , March 1999. *Approximation
and Complexity in Numerical Optimization: Continuous and Discrete Problems*
(P. M. Pardalos, Editor), Kluwer Academic Press, 2000, pp.489-500.

B-342: 小島政和, ``半正定値計画緩和と大域的最適化'', 1998年7月, 第１０回 RAMP シンポジウム論文集，195-204，1998年10月． RAMP シンポジウム発表用 OHP ps file ｜ pdf file．

B-341: M. Kojima and L. Tuncel, ``Discretization and Localization in Successive
Convex Relaxation for Nonconvex Quadratic Optimization Problems,'' July
1998. Revised May 2000. *Mathematical Programming *Vol.89, No.1, 79-111
(2000).

B-340: M. Kojima and L. Tuncel, ``Monotonicity of Primal-Dual Interior-Point
Algorithms for Semidefinite Programming Problems,'' May
1998, *Optimization Methods and Software *dedicated to the 65th birthday
of Professor Masao Iri, Vol. 10, Number 2, 275-296 (December, 1998).

B-339: 中田和秀，藤沢克樹，小島政和， ``半正定値計画問題に対する主双対内点法における共役勾配法の実装'', 1998年4月, 統計数理 Vol 46, No.2, 297-316 (1998年12月)．

B-338: M. Kojima and L. Tuncel, ``Cones of Matrices and Successive Convex Relaxations
of Nonconvex Sets,'' March 1998. Revised June
1999. *SIAM Journal on Optimization* Vol.10, No. 3, 750-778 (2000).

B-331: 小島政和, ``半正定値計画とその組合せ最適化への応用'', 1997年9月, 離散構造とアルゴリズム，藤重悟編，近代科学社，1998年6月．

B-330: K. Fujisawa, M. Fukuda, M. Kojima and K. Nakata, ``Numerical Evaluation
of SDPA (SemiDefinite Programming Algorithm),''
*High Performance Optimization*, H.Frenk, K. Roos, T. Terlaky and S. Zhang
eds., Kluwer Academic Press, 1999, pp.267-301.

B-327: M. Kojima, M. Shida and S. Shindoh, ``Search Directions in the SDP and
the Monotone SDLCP: Generalization and Inexact Computation,'' March
1997, *Mathematical Programming V*ol 85, No.1, 51-80 (May, 1999).

B-324: K. Fujisawa, M. Kojima and K. Nakata, ``Exploiting Sparsity in Primal-Dual
Interior-Point Methods for Semidefinite Programming'', *Mathematical Programming,
*Vol. 79, 235-253 (1997).

B-314: 小島政和, ``半正定値計画問題と内点法'', 1996年4月, 応用数理
Vol. 6, 16-25 (1996) .

B-313: M. Kojima, M. Shida and S. Shindoh, ``A Note on Nesterov-Todd and Kojima-Shindoh-Hara
Search Directions in Semidefinite Programming,'' April 1996, *Optimization
Methods and Software *Vol.11&12, 47-52 (December, 1999)*.*

B-312: M. Shida and S. Shindoh, ``Monotone Semidefinite Complementarity Problems,'' April 1996.

B-311: M. Kojima, M. Shida and S. Shindoh, ``A Predictor-Corrector Interior-Point
Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton
Search Direction'' , SIAM *Journal on Optimization
*Vol.9, No.2, 444-465*.*

B-310: M. Shida, S. Shindoh and M. Kojima, ``Existence of Search Direction
in Interior-Point Algorithms for the SDP and the Monotone SDLCP,'' January 1996.
SIAM *Journal on Optimization, *Vol.8,
387-396 (1998).

B-308: K. Fujisawa, M. Kojima, K. Nakata and M. Yamashita, ``SDPA (Semidefinite Programming Algorithm) User's Manual --- Version 6.0, '' December 1995, Revised July 2002. ps file, ps.gz file, pdf file

B-306: M. Kojima, M. Shida and S. Shindoh, ``Local Convergence of Predictor-Corrector
Infeasible-Interior-Point Algorithms for SDPs and SDLCPs,'' December 1995, Revised
October 1996. *Mathematical Programming, *Vol. 80, 129-161 (1998).

Appendix: Mathematica Program Used in Example
3.3

B-303: M. Shida, S. Shindoh and M. Kojima, ``Centers of Monotone Generalized
Complementarity Problems'',*Mathematics
of Operations Research, *Vol. 22, 969-976 (1997)

B-298: T. Fujie and M. Kojima, ``Semidefinite Programming Relaxation for Nonconvex
Quadratic Programs'', *Journal of Global Optimization, *Vol. 10 (1997)
pp.367-380.

B-296: M. Kojima, M. Shida and S. Shindoh, ``Reduction of Monotone Linear Complementarity
Problems over Cones to Linear Programs over *Cones'' , Acta Mathematica Vietnamica,
*Vol. 22, 147-157 (1997).

B-293: M. Kojima, ``A Primitive Interior Point Algorithm for Semidefinite Programs in Mathematica,'' December 1994.

B-290: M. Kojima, S. Kojima and S. Hara, ``Linear Algebra for Semidefinite Programming'' , 京都大学数理解析研究所講究録1004 (1997) pp.1- 23.

B-282: M. Kojima, S. Shindoh and S. Hara, ``Interior-Point Methods for the
Monotone Linear Complementarity Problem in Symmetric Matrices,'' *SIAM Journal
on Optimization*, Vol.7, 86-125 (1997).

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