{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:14:49Z","timestamp":1763388889916,"version":"3.40.3"},"publisher-location":"Cham","reference-count":46,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319065687"},{"type":"electronic","value":"9783319065694"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-06569-4_3","type":"book-chapter","created":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T20:16:15Z","timestamp":1397247375000},"page":"37-63","source":"Crossref","is-referenced-by-count":7,"title":["DC Programming Approaches for BMI and QMI Feasibility Problems"],"prefix":"10.1007","author":[{"given":"Yi-Shuai","family":"Niu","sequence":"first","affiliation":[]},{"given":"Tao Pham","family":"Dinh","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"2","key":"3_CR1","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1137\/S1052623497328008","volume":"10","author":"S.T. Benson","year":"2000","unstructured":"Benson, S.T., Ye, Y.Y.: DSDP: A complete description of the algorithm and a proof of convergence can be found in Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization. SIAM Journal on Optimization\u00a010(2), 443\u2013461 (2000), \n                      http:\/\/www.mcs.anl.gov\/hs\/software\/DSDP\/","journal-title":"SIAM Journal on Optimization"},{"key":"3_CR2","doi-asserted-by":"crossref","unstructured":"Beran, E.B., Vandenberghe, L., Boyd, S.: A global BMI algorithm based on the generalized Benders decomposition. In: Proceedings of the European Control Conference, Brussels, Belgium (July 1997)","DOI":"10.23919\/ECC.1997.7082698"},{"key":"3_CR3","unstructured":"Borchers, B.: CSDP: a C library for semidefinite programming, Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM (November 1998), \n                      https:\/\/projects.coin-or.org\/Csdp\/"},{"key":"3_CR4","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/BF00939667","volume":"78","author":"C.A. Floudas","year":"1993","unstructured":"Floudas, C.A., Visweswaran, V.: A primal-relaxed dual global optimization approach. Journal of Optimization Theory and Applications\u00a078, 187\u2013225 (1993)","journal-title":"Journal of Optimization Theory and Applications"},{"key":"3_CR5","doi-asserted-by":"crossref","first-page":"616","DOI":"10.9746\/sicetr1965.33.616","volume":"33","author":"H. Fujioka","year":"1997","unstructured":"Fujioka, H., Hoshijima, K.: Bounds for the BMI eingenvalue problem - a good lower bound and a cheap upper bound. Transactions of the Society of Instrument and Control Engineers\u00a033, 616\u2013621 (1997)","journal-title":"Transactions of the Society of Instrument and Control Engineers"},{"key":"3_CR6","unstructured":"Fujisawa, K., Kojima, M., Nakata, K.: SDPA (SemiDefinite Programming Algorithm) - user\u2019s manual - version 6.20. Research Report B-359, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan (January 2005), \n                      http:\/\/sdpa.indsys.chuo-u.ac.jp\/sdpa\/download.html\n                     (revised May 2005)"},{"issue":"1","key":"3_CR7","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1023\/A:1011224403708","volume":"19","author":"M. Fukuda","year":"2001","unstructured":"Fukuda, M., Kojima, M.: Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem. Computational Optimization and Applications\u00a019(1), 79\u2013105 (2001)","journal-title":"Computational Optimization and Applications"},{"key":"3_CR8","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF01099648","volume":"7","author":"K.C. Goh","year":"1995","unstructured":"Goh, K.C., Safonov, M.G., Papavassilopoulos, G.P.: Global optimization for the biaffine matrix inequality problem. Journal of Global Optimization\u00a07, 365\u2013380 (1995)","journal-title":"Journal of Global Optimization"},{"key":"3_CR9","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1002\/(SICI)1099-1239(199611)6:9\/10<1079::AID-RNC270>3.0.CO;2-#","volume":"6","author":"K.C. Goh","year":"1996","unstructured":"Goh, K.C., Safonov, M.G., Ly, J.H.: Robust synthesis via bilinear matrix inequalities. International Journal of Robust and Nonlinear Control\u00a06, 1079\u20131095 (1996)","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"3_CR10","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/978-1-4615-2025-2","volume-title":"Handbook of Global Optimization","author":"R. Horst","year":"1995","unstructured":"Horst, R.: D.C. Optimization: Theory, Methods and Algorithms. In: Horst, R., Pardalos, P.M. (eds.) Handbook of Global Optimization, pp. 149\u2013216. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"3_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1021765131316","volume":"103","author":"R. Horst","year":"1999","unstructured":"Horst, R., Thoai, N.V.: DC Programming: Overview. Journal of Optimization Theory and Applications\u00a0103, 1\u201343 (1999)","journal-title":"Journal of Optimization Theory and Applications"},{"key":"3_CR12","volume-title":"Convex Analysis and Minimization Algorithms","author":"J.B. Hiriart Urruty","year":"1993","unstructured":"Hiriart Urruty, J.B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms. Springer, Heidelberg (1993)"},{"key":"3_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0015-5","volume-title":"Introduction to Global Optimization","author":"R. Horst","year":"2000","unstructured":"Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization, 2nd edn. Kluwer Academic Publishers, Netherlands (2000)","edition":"2"},{"key":"3_CR14","unstructured":"Kawanishi, M., Sugie, T., Kanki, H.: BMI global optimization based on branch and bound method taking account of the property of local minima. In: Proceedings of the Conference on Decision and Control, San Diego, CA (December 1997)"},{"key":"3_CR15","unstructured":"Ko\u010dvara, M., Stingl, M.: PENBMI User\u2019s Guide (Version 2.1) (February 16, 2006)"},{"key":"3_CR16","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1008288411710","volume":"11","author":"H.A. Le Thi","year":"1997","unstructured":"Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by DC Algorithms. Journal of Global Optimization\u00a011, 253\u2013285 (1997)","journal-title":"Journal of Global Optimization"},{"issue":"2","key":"3_CR17","first-page":"169","volume":"27","author":"H.A. Le Thi","year":"1999","unstructured":"Le Thi, H.A., Pham Dinh, T., Le Dung, M.: Exact penalty in d.c. programming. Vietnam Journal of Mathematics\u00a027(2), 169\u2013178 (1999)","journal-title":"Vietnam Journal of Mathematics"},{"issue":"3","key":"3_CR18","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s101070050003","volume":"87","author":"H.A. Le Thi","year":"2000","unstructured":"Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Mathematical Programming Ser. A.\u00a087(3), 401\u2013426 (2000)","journal-title":"Mathematical Programming Ser. A."},{"issue":"3","key":"3_CR19","first-page":"1","volume":"45","author":"H.A. Le Thi","year":"2001","unstructured":"Le Thi, H.A., Pham Dinh, T.: A continuous approach for large-scale constrained quadratic zero-one programming (In honor of Professor ELSTER, Founder of the Journal Optimization). Optimization\u00a045(3), 1\u201328 (2001)","journal-title":"Optimization"},{"issue":"1","key":"3_CR20","first-page":"77","volume":"4","author":"H.A. Le Thi","year":"2003","unstructured":"Le Thi, H.A., Pham Dinh, T.: Large Scale Molecular Optimization From Distance Matrices by a D.C. Optimization Approach. SIAM Journal on Optimization\u00a04(1), 77\u2013116 (2003)","journal-title":"SIAM Journal on Optimization"},{"issue":"4","key":"3_CR21","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1023\/A:1026016804633","volume":"27","author":"H.A. Le Thi","year":"2003","unstructured":"Le Thi, H.A.: Solving large scale molecular distance geometry problems by a smoothing technique via the gaussian transform and d.c. programming. Journal of Global Optimization\u00a027(4), 375\u2013397 (2003)","journal-title":"Journal of Global Optimization"},{"issue":"4","key":"3_CR22","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1080\/10556780802263990","volume":"23","author":"H.A. Le Thi","year":"2008","unstructured":"Le Thi, H.A., Pham Dinh, T., Fran\u00e7ois, A.: Combining DCA and Interior Point Techniques for large-scale Nonconvex Quadratic Programming. Optimization Methods & Software\u00a023(4), 609\u2013629 (2008)","journal-title":"Optimization Methods & Software"},{"key":"3_CR23","doi-asserted-by":"crossref","unstructured":"Liu, S.M., Papavassilopoulos, G.P.: Numerical experience with parallel algorithms for solving the BMI problem. In: 13th Triennial World Congress of IFAC, San Francisco, CA (July 1996)","DOI":"10.1016\/S1474-6670(17)57935-5"},{"key":"3_CR24","unstructured":"L\u00f6fberg, J.: YALMIP: A Toolbox for Modeling and Optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan (2004), \n                      http:\/\/control.ee.ethz.ch\/~joloef\/wiki\/pmwiki.php"},{"key":"3_CR25","unstructured":"MATLAB R2007a: Documentation and User Guides, \n                      http:\/\/www.mathworks.com\/"},{"key":"3_CR26","first-page":"247","volume":"77","author":"M. Mesbahi","year":"1997","unstructured":"Mesbahi, M., Papavassilopoulos, G.P.: A cone programming approach to the bilinear matrix inequality problem and its geometry. Mathematical Programming\u00a077, 247\u2013272 (1997)","journal-title":"Mathematical Programming"},{"key":"3_CR27","unstructured":"Mittelmann, H.D.: Several SDP-codes on problems from SDPLIB, \n                      http:\/\/plato.asu.edu\/ftp\/sdplib.html"},{"key":"3_CR28","series-title":"CCIS","first-page":"244","volume-title":"MCO 2008","author":"Y.S. Niu","year":"2008","unstructured":"Niu, Y.S., Pham Dinh, T.: A DC Programming Approach for Mixed-Integer Linear Programs. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) MCO 2008. CCIS, vol.\u00a014, pp. 244\u2013253. Springer, Heidelberg (2008)"},{"key":"3_CR29","unstructured":"Niu, Y.S.: DC programming and DCA combinatorial optimization and polynomial optimization via SDP techniques, National Institute of Applied Sciences, Rouen, France (2010)"},{"issue":"3","key":"3_CR30","first-page":"525","volume":"50","author":"Y.S. Niu","year":"2010","unstructured":"Niu, Y.S., Pham Dinh, T.: An Efficient DC Programming Approach for Portfolio Decision with Higher Moments. Computational Optimization and Applications\u00a050(3), 525\u2013554 (2010)","journal-title":"Computational Optimization and Applications"},{"key":"3_CR31","unstructured":"Niu, Y.S., Pham Dinh, T.: Efficient DC programming approaches for mixed-integer quadratic convex programs. In: Proceedings of the International Conference on Industrial Engineering and Systems Management (IESM 2011), Metz, France, pp. 222\u2013231 (2011)"},{"issue":"4","key":"3_CR32","doi-asserted-by":"publisher","first-page":"812","DOI":"10.1080\/10556788.2011.645543","volume":"28","author":"Y.S. Niu","year":"2013","unstructured":"Niu, Y.S., Pham Dinh, T., Le Thi, H.A., Judice, J.J.: Efficient DC Programming Approaches for the Asymmetric Eigenvalue Complementarity Problem. Optimization Methods and Software\u00a028(4), 812\u2013829 (2013)","journal-title":"Optimization Methods and Software"},{"issue":"1","key":"3_CR33","first-page":"289","volume":"22","author":"T. Pham Dinh","year":"1997","unstructured":"Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to D.C. programming: Theory, Algorithms and Applications. Acta Mathematica Vietnamica\u00a022(1), 289\u2013355 (1997)","journal-title":"Acta Mathematica Vietnamica"},{"key":"3_CR34","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1137\/S1052623494274313","volume":"8","author":"T. Pham Dinh","year":"1998","unstructured":"Pham Dinh, T., Le Thi, H.A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optimization\u00a08, 476\u2013507 (1998)","journal-title":"SIAM J. Optimization"},{"key":"3_CR35","unstructured":"Pham Dinh, T., Le Thi, H.A.: DC Programming. Theory, Algorithms, Applications: The State of the Art. In: First International Workshop on Global Constrained Optimization and Constraint Satisfaction, Nice, October 2-4 (2002)"},{"key":"3_CR36","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"T. Pham Dinh","year":"2005","unstructured":"Pham Dinh, T., Le Thi, H.A.: The DC programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems. Annals of Operations Research\u00a0133, 23\u201346 (2005)","journal-title":"Annals of Operations Research"},{"key":"3_CR37","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, N.J. (1970)"},{"key":"3_CR38","unstructured":"Safonov, M.G., Goh, K.C., Ly, J.H.: Control system synthesis via bilinear matrix inequalities. In: Proceedings of the American Control Conference, Baltimore, MD (June 1994)"},{"key":"3_CR39","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/BF00122429","volume":"2","author":"H.D. Sherali","year":"1992","unstructured":"Sherali, H.D., Alameddine, A.R.: A new reformulation-linearization technique for bilinear programming problems. Journal of Global Optimization\u00a02, 379\u2013410 (1992)","journal-title":"Journal of Global Optimization"},{"key":"3_CR40","unstructured":"Sturm, J.F.: SeDuMi 1.2: a MATLAB toolbox for optimization over symmetric cones. Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands (August 1998), \n                      http:\/\/sedumi.ie.lehigh.edu\/"},{"key":"3_CR41","doi-asserted-by":"crossref","first-page":"701","DOI":"10.9746\/sicetr1965.33.701","volume":"33","author":"S. Takano","year":"1997","unstructured":"Takano, S., Watanabe, T., Yasuda, K.: Branch and bound technique for global solution of BMI. Transactions of the Society of Instrument and Control Engineers\u00a033, 701\u2013708 (1997)","journal-title":"Transactions of the Society of Instrument and Control Engineers"},{"key":"3_CR42","unstructured":"Toker, O., \u00d6zbay, H.: On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. In: American Control Conference, Seattle, WA (1995)"},{"key":"3_CR43","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1109\/TAC.2000.880996","volume":"45","author":"H.D. Tuan","year":"2000","unstructured":"Tuan, H.D., Hosoe, S., Tuy, H.: D.C. optimization approach to robust controls: Feasibility problems. IEEE Transactions on Automatic Control\u00a045, 1903\u20131909 (2000)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"3_CR44","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1002\/1099-1239(200006)10:7<561::AID-RNC493>3.0.CO;2-C","volume":"10","author":"H.D. Tuan","year":"2000","unstructured":"Tuan, H.D., Apkarian, P., Nakashima, Y.: A new Lagrangian dual global optimization algorithm for solving bilinear matrix inequalities. International Journal of Robust and Nonlinear Control\u00a010, 561\u2013578 (2000)","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"3_CR45","unstructured":"Van Antwerp, J.G.: Globally optimal robust control for systems with time-varying nonlinear perturbations. Master thesis, University of Illinois at Urbana-Champaign, Urbana, IL (1997)"},{"key":"3_CR46","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4381-7","volume-title":"Handbook of Semidefinite Programming - Theory, Algorithms, and Applications","author":"H. Wolkowicz","year":"2000","unstructured":"Wolkowicz, H., Saigal, R., Vandenberghe, L.: Handbook of Semidefinite Programming - Theory, Algorithms, and Applications. Kluwer Academic Publishers, USA (2000)"}],"container-title":["Advances in Intelligent Systems and Computing","Advanced Computational Methods for Knowledge Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-06569-4_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:30:06Z","timestamp":1675816206000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-06569-4_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319065687","9783319065694"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-06569-4_3","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2014]]}}}