Locatelli, M. A new technique to derive tight convex underestimators (sometimes envelopes). (English) Zbl 07806003 Comput. Optim. Appl. 87, No. 2, 475-499 (2024). MSC: 90Cxx PDFBibTeX XMLCite \textit{M. Locatelli}, Comput. Optim. Appl. 87, No. 2, 475--499 (2024; Zbl 07806003) Full Text: DOI OA License
Lindberg, Julia; Rodriguez, Jose Israel Invariants of SDP exactness in quadratic programming. (English) Zbl 07783989 J. Symb. Comput. 122, Article ID 102258, 18 p. (2024). MSC: 90Cxx 14Pxx 14Qxx PDFBibTeX XMLCite \textit{J. Lindberg} and \textit{J. I. Rodriguez}, J. Symb. Comput. 122, Article ID 102258, 18 p. (2024; Zbl 07783989) Full Text: DOI arXiv
Azuma, Godai; Fukuda, Mituhiro; Kim, Sunyoung; Yamashita, Makoto Exact SDP relaxations for quadratic programs with bipartite graph structures. (English) Zbl 1522.90063 J. Glob. Optim. 86, No. 3, 671-691 (2023). MSC: 90C20 90C22 90C25 90C26 PDFBibTeX XMLCite \textit{G. Azuma} et al., J. Glob. Optim. 86, No. 3, 671--691 (2023; Zbl 1522.90063) Full Text: DOI arXiv
Zhang, Bo; Gao, YueLin; Liu, Xia; Huang, XiaoLi Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems. (English) Zbl 1518.90059 J. Glob. Optim. 86, No. 1, 61-92 (2023). MSC: 90C20 90C26 90C30 PDFBibTeX XMLCite \textit{B. Zhang} et al., J. Glob. Optim. 86, No. 1, 61--92 (2023; Zbl 1518.90059) Full Text: DOI
Sheen, Heejune; Yamashita, Makoto Exploiting aggregate sparsity in second-order cone relaxations for quadratic constrained quadratic programming problems. (English) Zbl 1501.90063 Optim. Methods Softw. 37, No. 2, 753-771 (2022). MSC: 90C20 90C22 90C25 90C26 PDFBibTeX XMLCite \textit{H. Sheen} and \textit{M. Yamashita}, Optim. Methods Softw. 37, No. 2, 753--771 (2022; Zbl 1501.90063) Full Text: DOI arXiv
Cifuentes, Diego; Agarwal, Sameer; Parrilo, Pablo A.; Thomas, Rekha R. On the local stability of semidefinite relaxations. (English) Zbl 1494.90067 Math. Program. 193, No. 2 (B), 629-663 (2022). MSC: 90C22 90C31 PDFBibTeX XMLCite \textit{D. Cifuentes} et al., Math. Program. 193, No. 2 (B), 629--663 (2022; Zbl 1494.90067) Full Text: DOI arXiv
Azuma, Godai; Fukuda, Mituhiro; Kim, Sunyoung; Yamashita, Makoto Exact SDP relaxations of quadratically constrained quadratic programs with forest structures. (English) Zbl 1486.90138 J. Glob. Optim. 82, No. 2, 243-262 (2022). MSC: 90C20 90C22 PDFBibTeX XMLCite \textit{G. Azuma} et al., J. Glob. Optim. 82, No. 2, 243--262 (2022; Zbl 1486.90138) Full Text: DOI arXiv
Locatelli, Marco; Schoen, Fabio (Global) optimization: historical notes and recent developments. (English) Zbl 07711233 EURO J. Comput. Optim. 9, Article ID 100012, 15 p. (2021). MSC: 90C26 90-02 90-03 90C30 PDFBibTeX XMLCite \textit{M. Locatelli} and \textit{F. Schoen}, EURO J. Comput. Optim. 9, Article ID 100012, 15 p. (2021; Zbl 07711233) Full Text: DOI
Luo, Hezhi; Chen, Sikai; Wu, Huixian A new branch-and-cut algorithm for non-convex quadratic programming via alternative direction method and semidefinite relaxation. (English) Zbl 1489.65087 Numer. Algorithms 88, No. 2, 993-1024 (2021). MSC: 65K05 90C20 90C22 90C26 90C57 PDFBibTeX XMLCite \textit{H. Luo} et al., Numer. Algorithms 88, No. 2, 993--1024 (2021; Zbl 1489.65087) Full Text: DOI
Adjé, Assalé Quadratic maximization of reachable values of affine systems with diagonalizable matrix. (English) Zbl 1470.90062 J. Optim. Theory Appl. 189, No. 1, 136-163 (2021). MSC: 90C20 PDFBibTeX XMLCite \textit{A. Adjé}, J. Optim. Theory Appl. 189, No. 1, 136--163 (2021; Zbl 1470.90062) Full Text: DOI arXiv
Wang, Yuzhu; Tanaka, Akihiro; Yoshise, Akiko Polyhedral approximations of the semidefinite cone and their application. (English) Zbl 1469.90105 Comput. Optim. Appl. 78, No. 3, 893-913 (2021). MSC: 90C22 PDFBibTeX XMLCite \textit{Y. Wang} et al., Comput. Optim. Appl. 78, No. 3, 893--913 (2021; Zbl 1469.90105) Full Text: DOI arXiv
Madani, Ramtin; Kheirandishfard, Mohsen; Lavaei, Javad; Atamtürk, Alper Penalized semidefinite programming for quadratically-constrained quadratic optimization. (English) Zbl 1462.65068 J. Glob. Optim. 78, No. 3, 423-451 (2020). MSC: 65K05 90C26 90C22 PDFBibTeX XMLCite \textit{R. Madani} et al., J. Glob. Optim. 78, No. 3, 423--451 (2020; Zbl 1462.65068) Full Text: DOI arXiv
Staib, Matthew; Jegelka, Stefanie Robust budget allocation via continuous submodular functions. (English) Zbl 1465.90057 Appl. Math. Optim. 82, No. 3, 1049-1079 (2020). MSC: 90C17 90C26 91B32 PDFBibTeX XMLCite \textit{M. Staib} and \textit{S. Jegelka}, Appl. Math. Optim. 82, No. 3, 1049--1079 (2020; Zbl 1465.90057) Full Text: DOI arXiv
Xia, Wei; Vera, Juan C.; Zuluaga, Luis F. Globally solving nonconvex quadratic programs via linear integer programming techniques. (English) Zbl 07284452 INFORMS J. Comput. 32, No. 1, 40-56 (2020). MSC: 90Cxx PDFBibTeX XMLCite \textit{W. Xia} et al., INFORMS J. Comput. 32, No. 1, 40--56 (2020; Zbl 07284452) Full Text: DOI arXiv
Niazadeh, Rad; Roughgarden, Tim; Wang, Joshua R. Optimal algorithms for continuous non-monotone submodular and DR-submodular maximization. (English) Zbl 1520.65047 J. Mach. Learn. Res. 21, Paper No. 125, 31 p. (2020). MSC: 65K10 68T05 PDFBibTeX XMLCite \textit{R. Niazadeh} et al., J. Mach. Learn. Res. 21, Paper No. 125, 31 p. (2020; Zbl 1520.65047) Full Text: arXiv Link
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures. (English) Zbl 1444.90090 J. Glob. Optim. 77, No. 3, 513-541 (2020). MSC: 90C20 90C26 PDFBibTeX XMLCite \textit{S. Kim} et al., J. Glob. Optim. 77, No. 3, 513--541 (2020; Zbl 1444.90090) Full Text: DOI arXiv
Sadeghi, Ali; Saraj, Mansour; Mahdavi Amiri, Nezam Solving a fractional program with second order cone constraint. (English) Zbl 1455.90139 Iran. J. Math. Sci. Inform. 14, No. 2, 33-42 (2019). MSC: 90C32 90C46 PDFBibTeX XMLCite \textit{A. Sadeghi} et al., Iran. J. Math. Sci. Inform. 14, No. 2, 33--42 (2019; Zbl 1455.90139) Full Text: Link
Chuong, T. D.; Jeyakumar, V.; Li, G. A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs. (English) Zbl 1433.90122 J. Glob. Optim. 75, No. 4, 885-919 (2019). MSC: 90C26 90C22 PDFBibTeX XMLCite \textit{T. D. Chuong} et al., J. Glob. Optim. 75, No. 4, 885--919 (2019; Zbl 1433.90122) Full Text: DOI
Kimizuka, Masaki; Kim, Sunyoung; Yamashita, Makoto Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods. (English) Zbl 1433.90103 J. Glob. Optim. 75, No. 3, 631-654 (2019). MSC: 90C20 90C22 90C25 90C26 PDFBibTeX XMLCite \textit{M. Kimizuka} et al., J. Glob. Optim. 75, No. 3, 631--654 (2019; Zbl 1433.90103) Full Text: DOI arXiv
Bach, Francis Submodular functions: from discrete to continuous domains. (English) Zbl 1423.90174 Math. Program. 175, No. 1-2 (A), 419-459 (2019). MSC: 90C25 90C27 PDFBibTeX XMLCite \textit{F. Bach}, Math. Program. 175, No. 1--2 (A), 419--459 (2019; Zbl 1423.90174) Full Text: DOI arXiv HAL
Luo, Hezhi; Bai, Xiaodi; Lim, Gino; Peng, Jiming New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation. (English) Zbl 1411.90251 Math. Program. Comput. 11, No. 1, 119-171 (2019). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{H. Luo} et al., Math. Program. Comput. 11, No. 1, 119--171 (2019; Zbl 1411.90251) Full Text: DOI
Luo, Hezhi; Bai, Xiaodi; Peng, Jiming Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods. (English) Zbl 1409.90130 J. Optim. Theory Appl. 180, No. 3, 964-992 (2019). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{H. Luo} et al., J. Optim. Theory Appl. 180, No. 3, 964--992 (2019; Zbl 1409.90130) Full Text: DOI
Sadeghi, Ali; Saraj, Mansour; Mahdavi Amiri, Nezam Efficient solutions of interval programming problems with inexact parameters and second order cone constraints. (English) Zbl 1404.90137 Mathematics 6, No. 11, Paper No. 270, 13 p. (2018). MSC: 90C46 90C29 PDFBibTeX XMLCite \textit{A. Sadeghi} et al., Mathematics 6, No. 11, Paper No. 270, 13 p. (2018; Zbl 1404.90137) Full Text: DOI
Zheng, Xiaojin; Pan, Yutong; Cui, Xueting Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint. (English) Zbl 1417.90111 J. Glob. Optim. 70, No. 4, 719-735 (2018). MSC: 90C20 90C26 90C22 PDFBibTeX XMLCite \textit{X. Zheng} et al., J. Glob. Optim. 70, No. 4, 719--735 (2018; Zbl 1417.90111) Full Text: DOI
Kuang, Xiaolong; Zuluaga, Luis F. Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization. (English) Zbl 1403.90554 J. Glob. Optim. 70, No. 3, 551-577 (2018). Reviewer: Samir Kumar Neogy (New Delhi) MSC: 90C26 PDFBibTeX XMLCite \textit{X. Kuang} and \textit{L. F. Zuluaga}, J. Glob. Optim. 70, No. 3, 551--577 (2018; Zbl 1403.90554) Full Text: DOI arXiv
Polyak, Boris; Gryazina, Elena Convexity/nonconvexity certificates for power flow analysis. (English) Zbl 1397.90080 Bertsch, Valentin (ed.) et al., Advances in energy system optimization. Proceedings of the first international symposium on energy system optimization, ISECO, Heidelberg, Germany, November 9–10, 2015. Basel: Birkhäuser/Springer (ISBN 978-3-319-51794-0/hbk; 978-3-319-51795-7/ebook). Trends in Mathematics, 221-230 (2017). MSC: 90B10 90C20 PDFBibTeX XMLCite \textit{B. Polyak} and \textit{E. Gryazina}, in: Advances in energy system optimization. Proceedings of the first international symposium on energy system optimization, ISESO, Heidelberg, Germany, November 9--10, 2015. Basel: Birkhäuser/Springer. 221--230 (2017; Zbl 1397.90080) Full Text: DOI
Ahmadi, Amir Ali; Dash, Sanjeeb; Hall, Georgina Optimization over structured subsets of positive semidefinite matrices via column generation. (English) Zbl 1387.90179 Discrete Optim. 24, 129-151 (2017). MSC: 90C22 PDFBibTeX XMLCite \textit{A. A. Ahmadi} et al., Discrete Optim. 24, 129--151 (2017; Zbl 1387.90179) Full Text: DOI arXiv
Madani, Ramtin; Sojoudi, Somayeh; Fazelnia, Ghazal; Lavaei, Javad Finding low-rank solutions of sparse linear matrix inequalities using convex optimization. (English) Zbl 1365.90185 SIAM J. Optim. 27, No. 2, 725-758 (2017). MSC: 90C20 90C22 90C25 90C26 90C30 90C35 90C90 52A41 PDFBibTeX XMLCite \textit{R. Madani} et al., SIAM J. Optim. 27, No. 2, 725--758 (2017; Zbl 1365.90185) Full Text: DOI
Jin, Qingwei; Tian, Ye; Deng, Zhibin; Fang, Shu-Cherng; Xing, Wenxun Exact computable representation of some second-order cone constrained quadratic programming problems. (English) Zbl 1277.90091 J. Oper. Res. Soc. China 1, No. 1, 107-134 (2013). MSC: 90C22 90C60 PDFBibTeX XMLCite \textit{Q. Jin} et al., J. Oper. Res. Soc. China 1, No. 1, 107--134 (2013; Zbl 1277.90091) Full Text: DOI
Tuy, H.; Tuan, H. D. Generalized S-lemma and strong duality in nonconvex quadratic programming. (English) Zbl 1300.90020 J. Glob. Optim. 56, No. 3, 1045-1072 (2013). MSC: 90C10 90C20 90C22 PDFBibTeX XMLCite \textit{H. Tuy} and \textit{H. D. Tuan}, J. Glob. Optim. 56, No. 3, 1045--1072 (2013; Zbl 1300.90020) Full Text: DOI
Yang, Yuning; Yang, Qingzhi On solving biquadratic optimization via semidefinite relaxation. (English) Zbl 1285.90070 Comput. Optim. Appl. 53, No. 3, 845-867 (2012). MSC: 90C30 90C20 90C22 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{Q. Yang}, Comput. Optim. Appl. 53, No. 3, 845--867 (2012; Zbl 1285.90070) Full Text: DOI
Zheng, X. J.; Sun, X. L.; Li, D.; Xu, Y. F. On zero duality gap in nonconvex quadratic programming problems. (English) Zbl 1266.90151 J. Glob. Optim. 52, No. 2, 229-242 (2012). MSC: 90C26 90C20 90C46 PDFBibTeX XMLCite \textit{X. J. Zheng} et al., J. Glob. Optim. 52, No. 2, 229--242 (2012; Zbl 1266.90151) Full Text: DOI
Bayón, L.; Grau, J. M.; Ruiz, M. M.; Suárez, P. M. A quasi-linear algorithm for calculating the infimal convolution of convex quadratic functions. (English) Zbl 1237.65056 J. Comput. Appl. Math. 236, No. 12, 2990-2997 (2012). MSC: 65K05 90C20 90C25 90C60 PDFBibTeX XMLCite \textit{L. Bayón} et al., J. Comput. Appl. Math. 236, No. 12, 2990--2997 (2012; Zbl 1237.65056) Full Text: DOI
Zheng, X. J.; Sun, X. L.; Li, D. Nonconvex quadratically constrained quadratic programming: Best D.C. Decompositions and their SDP representations. (English) Zbl 1254.90151 J. Glob. Optim. 50, No. 4, 695-712 (2011). MSC: 90C20 90C26 PDFBibTeX XMLCite \textit{X. J. Zheng} et al., J. Glob. Optim. 50, No. 4, 695--712 (2011; Zbl 1254.90151) Full Text: DOI
Zheng, Xiao Jin; Sun, Xiao Ling; Li, Duan Convex relaxations for nonconvex quadratically constrained quadratic programming: matrix cone decomposition and polyhedral approximation. (English) Zbl 1236.90089 Math. Program. 129, No. 2 (B), 301-329 (2011). Reviewer: Stephan Dempe (Freiberg) MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{X. J. Zheng} et al., Math. Program. 129, No. 2 (B), 301--329 (2011; Zbl 1236.90089) Full Text: DOI
Mevissen, Martin; Kojima, Masakazu SDP relaxations for quadratic optimization problems derived from polynomial optimization problems. (English) Zbl 1186.90085 Asia-Pac. J. Oper. Res. 27, No. 1, 15-38 (2010). MSC: 90C20 90C22 PDFBibTeX XMLCite \textit{M. Mevissen} and \textit{M. Kojima}, Asia-Pac. J. Oper. Res. 27, No. 1, 15--38 (2010; Zbl 1186.90085) Full Text: DOI