Wang, Chunyan; Chen, Haibin; Wang, Yiju; Yan, Hong; Zhou, Guanglu Copositive tensor optimization problem and its applications to hypergraphs. (English) Zbl 07799951 J. Ind. Manag. Optim. 20, No. 3, 926-941 (2024). MSC: 58F15 58F17 53C35 PDFBibTeX XMLCite \textit{C. Wang} et al., J. Ind. Manag. Optim. 20, No. 3, 926--941 (2024; Zbl 07799951) Full Text: DOI
Bomze, Immanuel M.; Gabl, Markus Optimization under uncertainty and risk: quadratic and copositive approaches. (English) Zbl 07709828 Eur. J. Oper. Res. 310, No. 2, 449-476 (2023). MSC: 90Bxx PDFBibTeX XMLCite \textit{I. M. Bomze} and \textit{M. Gabl}, Eur. J. Oper. Res. 310, No. 2, 449--476 (2023; Zbl 07709828) Full Text: DOI
Zamani, Moslem New bounds for nonconvex quadratically constrained quadratic programming. (English) Zbl 1515.90092 J. Glob. Optim. 85, No. 3, 595-613 (2023). MSC: 90C20 90C26 PDFBibTeX XMLCite \textit{M. Zamani}, J. Glob. Optim. 85, No. 3, 595--613 (2023; Zbl 1515.90092) Full Text: DOI arXiv
Peng, Bo Performance comparison of two recently proposed copositivity tests. (English) Zbl 07711256 EURO J. Comput. Optim. 10, Article ID 100037, 11 p. (2022). MSC: 90C20 15B48 90C11 90C59 PDFBibTeX XMLCite \textit{B. Peng}, EURO J. Comput. Optim. 10, Article ID 100037, 11 p. (2022; Zbl 07711256) Full Text: DOI
Bisori, Riccardo; Lapucci, Matteo; Sciandrone, Marco A study on sequential minimal optimization methods for standard quadratic problems. (English) Zbl 1507.90117 4OR 20, No. 4, 685-712 (2022). MSC: 90C20 PDFBibTeX XMLCite \textit{R. Bisori} et al., 4OR 20, No. 4, 685--712 (2022; Zbl 1507.90117) Full Text: DOI
Kirschner, Felix; de Klerk, Etienne Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere. (English) Zbl 1502.90118 Optim. Lett. 16, No. 8, 2191-2208 (2022). MSC: 90C22 90C05 PDFBibTeX XMLCite \textit{F. Kirschner} and \textit{E. de Klerk}, Optim. Lett. 16, No. 8, 2191--2208 (2022; Zbl 1502.90118) Full Text: DOI arXiv
G.-Tóth, B.; Hendrix, E. M. T.; Casado, L. G. On monotonicity and search strategies in face-based copositivity detection algorithms. (English) Zbl 07557119 CEJOR, Cent. Eur. J. Oper. Res. 30, No. 3, 1071-1092 (2022). MSC: 90Bxx PDFBibTeX XMLCite \textit{B. G. -Tóth} et al., CEJOR, Cent. Eur. J. Oper. Res. 30, No. 3, 1071--1092 (2022; Zbl 07557119) Full Text: DOI
Badenbroek, Riley; de Klerk, Etienne An analytic center cutting plane method to determine complete positivity of a matrix. (English) Zbl 07551228 INFORMS J. Comput. 34, No. 2, 1115-1125 (2022). MSC: 90-XX PDFBibTeX XMLCite \textit{R. Badenbroek} and \textit{E. de Klerk}, INFORMS J. Comput. 34, No. 2, 1115--1125 (2022; Zbl 07551228) Full Text: DOI arXiv
Bettiol, Enrico; Bomze, Immanuel; Létocart, Lucas; Rinaldi, Francesco; Traversi, Emiliano Mining for diamonds – matrix generation algorithms for binary quadratically constrained quadratic problems. (English) Zbl 1511.90319 Comput. Oper. Res. 142, Article ID 105735, 11 p. (2022). MSC: 90C22 90C09 90C20 90C26 PDFBibTeX XMLCite \textit{E. Bettiol} et al., Comput. Oper. Res. 142, Article ID 105735, 11 p. (2022; Zbl 1511.90319) Full Text: DOI
Gökmen, Y. Görkem; Yıldırım, E. Alper On standard quadratic programs with exact and inexact doubly nonnegative relaxations. (English) Zbl 1491.90111 Math. Program. 193, No. 1 (A), 365-403 (2022). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{Y. G. Gökmen} and \textit{E. A. Yıldırım}, Math. Program. 193, No. 1 (A), 365--403 (2022; Zbl 1491.90111) Full Text: DOI arXiv
Laurent, Monique; Vargas, Luis Felipe Finite convergence of sum-of-squares hierarchies for the stability number of a graph. (English) Zbl 1487.05259 SIAM J. Optim. 32, No. 2, 491-518 (2022). MSC: 05C99 90C20 90C22 90C26 90C27 11E25 PDFBibTeX XMLCite \textit{M. Laurent} and \textit{L. F. Vargas}, SIAM J. Optim. 32, No. 2, 491--518 (2022; Zbl 1487.05259) Full Text: DOI arXiv
Eichfelder, Gabriele; Groetzner, Patrick A note on completely positive relaxations of quadratic problems in a multiobjective framework. (English) Zbl 1486.90172 J. Glob. Optim. 82, No. 3, 615-626 (2022). MSC: 90C29 90C20 15B48 PDFBibTeX XMLCite \textit{G. Eichfelder} and \textit{P. Groetzner}, J. Glob. Optim. 82, No. 3, 615--626 (2022; Zbl 1486.90172) Full Text: DOI
Bomze, Immanuel M.; Gabl, Markus; Maggioni, Francesca; Pflug, Georg Ch. Two-stage stochastic standard quadratic optimization. (English) Zbl 1495.90114 Eur. J. Oper. Res. 299, No. 1, 21-34 (2022). MSC: 90C15 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., Eur. J. Oper. Res. 299, No. 1, 21--34 (2022; Zbl 1495.90114) Full Text: DOI
Deligkas, Argyrios; Fearnley, John; Melissourgos, Themistoklis; Spirakis, Paul G. Approximating the existential theory of the reals. (English) Zbl 07466700 J. Comput. Syst. Sci. 125, 106-128 (2022). MSC: 68-XX PDFBibTeX XMLCite \textit{A. Deligkas} et al., J. Comput. Syst. Sci. 125, 106--128 (2022; Zbl 07466700) Full Text: DOI arXiv
Dür, Mirjam; Rendl, Franz Conic optimization: a survey with special focus on copositive optimization and binary quadratic problems. (English) Zbl 1516.90043 EURO J. Comput. Optim. 9, Article ID 100021, 12 p. (2021). MSC: 90C22 90C20 90C27 PDFBibTeX XMLCite \textit{M. Dür} and \textit{F. Rendl}, EURO J. Comput. Optim. 9, Article ID 100021, 12 p. (2021; Zbl 1516.90043) Full Text: DOI
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
Bomze, Immanuel M.; Rinaldi, Francesco; Zeffiro, Damiano Frank-Wolfe and friends: a journey into projection-free first-order optimization methods. (English) Zbl 1479.90131 4OR 19, No. 3, 313-345 (2021). MSC: 90C06 90C25 90C30 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., 4OR 19, No. 3, 313--345 (2021; Zbl 1479.90131) Full Text: DOI arXiv
Gondzio, Jacek; Yıldırım, E. Alper Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations. (English) Zbl 1519.90147 J. Glob. Optim. 81, No. 2, 293-321 (2021). Reviewer: Reinhardt Euler (Brest) MSC: 90C20 90C11 90C26 PDFBibTeX XMLCite \textit{J. Gondzio} and \textit{E. A. Yıldırım}, J. Glob. Optim. 81, No. 2, 293--321 (2021; Zbl 1519.90147) Full Text: DOI arXiv
Ahmed, Faizan; Still, Georg Two methods for the maximization of homogeneous polynomials over the simplex. (English) Zbl 1478.90082 Comput. Optim. Appl. 80, No. 2, 523-548 (2021). MSC: 90C23 90C26 91A22 05C69 PDFBibTeX XMLCite \textit{F. Ahmed} and \textit{G. Still}, Comput. Optim. Appl. 80, No. 2, 523--548 (2021; Zbl 1478.90082) Full Text: DOI
Flores-Bazán, Fabián; González-Valencia, Luis Characterizing existence of minimizers and optimality to nonconvex quadratic integrals. (English) Zbl 1475.90056 J. Optim. Theory Appl. 188, No. 2, 497-522 (2021). Reviewer: Morteza Pakdaman (Mashhad) MSC: 90C25 90C26 PDFBibTeX XMLCite \textit{F. Flores-Bazán} and \textit{L. González-Valencia}, J. Optim. Theory Appl. 188, No. 2, 497--522 (2021; Zbl 1475.90056) Full Text: DOI
Bomze, Immanuel M.; Kahr, Michael; Leitner, Markus Trust your data or not – StQP remains StQP: community detection via robust standard quadratic optimization. (English) Zbl 1469.90097 Math. Oper. Res. 46, No. 1, 301-316 (2021). MSC: 90C17 90C20 90C47 90C35 90C30 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., Math. Oper. Res. 46, No. 1, 301--316 (2021; Zbl 1469.90097) Full Text: DOI
Bomze, Immanuel; Gabl, Markus Interplay of non-convex quadratically constrained problems with adjustable robust optimization. (English) Zbl 1462.90081 Math. Methods Oper. Res. 93, No. 1, 115-151 (2021). MSC: 90C20 90C17 PDFBibTeX XMLCite \textit{I. Bomze} and \textit{M. Gabl}, Math. Methods Oper. Res. 93, No. 1, 115--151 (2021; Zbl 1462.90081) Full Text: DOI
Chen, Xin; Pittel, Boris On sparsity of the solution to a random quadratic optimization problem. (English) Zbl 1459.90143 Math. Program. 186, No. 1-2 (A), 309-336 (2021). MSC: 90C20 90C26 15B52 PDFBibTeX XMLCite \textit{X. Chen} and \textit{B. Pittel}, Math. Program. 186, No. 1--2 (A), 309--336 (2021; Zbl 1459.90143) Full Text: DOI arXiv
Padmanabhan, Divya; Natarajan, Karthik; Murthy, Karthyek Exploiting partial correlations in distributionally robust optimization. (English) Zbl 1459.90140 Math. Program. 186, No. 1-2 (A), 209-255 (2021). MSC: 90C17 90C11 90C22 90-02 PDFBibTeX XMLCite \textit{D. Padmanabhan} et al., Math. Program. 186, No. 1--2 (A), 209--255 (2021; Zbl 1459.90140) Full Text: DOI arXiv
Anstreicher, Kurt M. Testing copositivity via mixed-integer linear programming. (English) Zbl 1459.90132 Linear Algebra Appl. 609, 218-230 (2021). MSC: 90C11 90C26 15B48 PDFBibTeX XMLCite \textit{K. M. Anstreicher}, Linear Algebra Appl. 609, 218--230 (2021; Zbl 1459.90132) Full Text: DOI
Bomze, Immanuel M.; Schachinger, Werner Constructing patterns of (many) ESSs under support size control. (English) Zbl 1461.91042 Dyn. Games Appl. 10, No. 3, 618-640 (2020). MSC: 91A22 90C20 PDFBibTeX XMLCite \textit{I. M. Bomze} and \textit{W. Schachinger}, Dyn. Games Appl. 10, No. 3, 618--640 (2020; Zbl 1461.91042) Full Text: DOI
Mittal, Areesh; Gokalp, Can; Hanasusanto, Grani A. Robust quadratic programming with mixed-integer uncertainty. (English) Zbl 1474.90312 INFORMS J. Comput. 32, No. 2, 201-218 (2020). MSC: 90C17 90C20 90C22 90C25 PDFBibTeX XMLCite \textit{A. Mittal} et al., INFORMS J. Comput. 32, No. 2, 201--218 (2020; Zbl 1474.90312) Full Text: DOI arXiv
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan A geometrical analysis on convex conic reformulations of quadratic and polynomial optimization problems. (English) Zbl 1491.90112 SIAM J. Optim. 30, No. 2, 1251-1273 (2020). MSC: 90C20 90C23 90C25 90C26 PDFBibTeX XMLCite \textit{S. Kim} et al., SIAM J. Optim. 30, No. 2, 1251--1273 (2020; Zbl 1491.90112) Full Text: DOI arXiv
Flores-Bazán, Fabián; Cárcamo, Gabriel; Caro, Stephanie Extensions of the standard quadratic optimization problem: strong duality, optimality, hidden convexity and S-lemma. (English) Zbl 1464.90049 Appl. Math. Optim. 81, No. 2, 383-408 (2020). MSC: 90C20 90C26 90C39 90C46 49N15 PDFBibTeX XMLCite \textit{F. Flores-Bazán} et al., Appl. Math. Optim. 81, No. 2, 383--408 (2020; Zbl 1464.90049) Full Text: DOI
Gouveia, João; Pong, Ting Kei; Saee, Mina Inner approximating the completely positive cone via the cone of scaled diagonally dominant matrices. (English) Zbl 1435.90114 J. Glob. Optim. 76, No. 2, 383-405 (2020). MSC: 90C26 90C59 PDFBibTeX XMLCite \textit{J. Gouveia} et al., J. Glob. Optim. 76, No. 2, 383--405 (2020; Zbl 1435.90114) Full Text: DOI arXiv
Amaral, Paula Alexandra; Bomze, Immanuel M. Nonconvex min-max fractional quadratic problems under quadratic constraints: copositive relaxations. (English) Zbl 1434.90216 J. Glob. Optim. 75, No. 2, 227-245 (2019). MSC: 90C47 90C22 90C26 90C32 PDFBibTeX XMLCite \textit{P. A. Amaral} and \textit{I. M. Bomze}, J. Glob. Optim. 75, No. 2, 227--245 (2019; Zbl 1434.90216) Full Text: DOI
Ahmadi, Amir Ali; Majumdar, Anirudha DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization. (English) Zbl 1465.90061 SIAM J. Appl. Algebra Geom. 3, No. 2, 193-230 (2019). MSC: 90C25 90C22 65K05 12E05 93C85 14P10 PDFBibTeX XMLCite \textit{A. A. Ahmadi} and \textit{A. Majumdar}, SIAM J. Appl. Algebra Geom. 3, No. 2, 193--230 (2019; Zbl 1465.90061) Full Text: DOI arXiv
Ahmed, Faizan; Still, Georg Maximization of homogeneous polynomials over the simplex and the sphere: structure, stability, and generic behavior. (English) Zbl 1414.90279 J. Optim. Theory Appl. 181, No. 3, 972-996 (2019). MSC: 90C26 90C31 90C46 91A22 PDFBibTeX XMLCite \textit{F. Ahmed} and \textit{G. Still}, J. Optim. Theory Appl. 181, No. 3, 972--996 (2019; Zbl 1414.90279) Full Text: DOI
Dickinson, Peter J. C. A new certificate for copositivity. (English) Zbl 1414.15042 Linear Algebra Appl. 569, 15-37 (2019). MSC: 15B48 65F30 90C25 PDFBibTeX XMLCite \textit{P. J. C. Dickinson}, Linear Algebra Appl. 569, 15--37 (2019; Zbl 1414.15042) Full Text: DOI
Liuzzi, G.; Locatelli, M.; Piccialli, Veronica A new branch-and-bound algorithm for standard quadratic programming problems. (English) Zbl 1405.90144 Optim. Methods Softw. 34, No. 1, 79-97 (2019). MSC: 90C57 90C20 PDFBibTeX XMLCite \textit{G. Liuzzi} et al., Optim. Methods Softw. 34, No. 1, 79--97 (2019; Zbl 1405.90144) Full Text: DOI
Hanasusanto, Grani A.; Kuhn, Daniel Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls. (English) Zbl 1455.90121 Oper. Res. 66, No. 3, 849-869 (2018). MSC: 90C17 90C30 PDFBibTeX XMLCite \textit{G. A. Hanasusanto} and \textit{D. Kuhn}, Oper. Res. 66, No. 3, 849--869 (2018; Zbl 1455.90121) Full Text: DOI arXiv
Deligkas, Argyrios; Fearnley, John; Melissourgos, Themistoklis; Spirakis, Paul G. Approximating the existential theory of the reals. (English) Zbl 1443.91012 Christodoulou, George (ed.) et al., Web and Internet economics. 14th international conference, WINE 2018, Oxford, UK, December 15–17, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11316, 126-139 (2018). MSC: 91A10 91A15 PDFBibTeX XMLCite \textit{A. Deligkas} et al., Lect. Notes Comput. Sci. 11316, 126--139 (2018; Zbl 1443.91012) Full Text: DOI arXiv
Bomze, Immanuel M.; Schachinger, Werner; Ullrich, Reinhard The complexity of simple models – a study of worst and typical hard cases for the standard quadratic optimization problem. (English) Zbl 1440.90042 Math. Oper. Res. 43, No. 2, 651-674 (2018). MSC: 90C20 90C26 91A22 92D25 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., Math. Oper. Res. 43, No. 2, 651--674 (2018; Zbl 1440.90042) Full Text: DOI
Ito, N.; Kim, Sunyoung; Kojima, M.; Takeda, A.; Toh, K.-C. Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems. (English) Zbl 1404.90096 J. Glob. Optim. 72, No. 4, 619-653 (2018). MSC: 90C20 90C22 90C25 90C26 PDFBibTeX XMLCite \textit{N. Ito} et al., J. Glob. Optim. 72, No. 4, 619--653 (2018; Zbl 1404.90096) Full Text: DOI
Prasad, Madhushini Narayana; Hanasusanto, Grani A. Improved conic reformulations for \(K\)-means clustering. (English) Zbl 1408.90237 SIAM J. Optim. 28, No. 4, 3105-3126 (2018). MSC: 90C25 90C22 90C26 PDFBibTeX XMLCite \textit{M. N. Prasad} and \textit{G. A. Hanasusanto}, SIAM J. Optim. 28, No. 4, 3105--3126 (2018; Zbl 1408.90237) Full Text: DOI arXiv
Tanaka, Akihiro; Yoshise, Akiko LP-based tractable subcones of the semidefinite plus nonnegative cone. (English) Zbl 1423.90139 Ann. Oper. Res. 265, No. 1, 155-182 (2018). MSC: 90C05 PDFBibTeX XMLCite \textit{A. Tanaka} and \textit{A. Yoshise}, Ann. Oper. Res. 265, No. 1, 155--182 (2018; Zbl 1423.90139) Full Text: DOI arXiv
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
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
Ling, Chen; He, Hongjin; Qi, Liqun Improved approximation results on standard quartic polynomial optimization. (English) Zbl 1410.90167 Optim. Lett. 11, No. 8, 1767-1782 (2017). MSC: 90C26 90C59 PDFBibTeX XMLCite \textit{C. Ling} et al., Optim. Lett. 11, No. 8, 1767--1782 (2017; Zbl 1410.90167) Full Text: DOI
de Klerk, Etienne; Laurent, Monique; Sun, Zhao; Vera, Juan C. On the convergence rate of grid search for polynomial optimization over the simplex. (English) Zbl 1394.90473 Optim. Lett. 11, No. 3, 597-608 (2017). MSC: 90C26 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Optim. Lett. 11, No. 3, 597--608 (2017; Zbl 1394.90473) Full Text: DOI arXiv Link
Lasserre, Jean B. A MAX-CUT formulation of 0/1 programs. (English) Zbl 1408.90222 Oper. Res. Lett. 44, No. 2, 158-164 (2016). MSC: 90C20 90C10 90C22 PDFBibTeX XMLCite \textit{J. B. Lasserre}, Oper. Res. Lett. 44, No. 2, 158--164 (2016; Zbl 1408.90222) Full Text: DOI arXiv
Bai, Lijie; Mitchell, John E.; Pang, Jong-Shi On conic QPCCs, conic QCQPs and completely positive programs. (English) Zbl 1346.90624 Math. Program. 159, No. 1-2 (A), 109-136 (2016). MSC: 90C11 90C22 90C25 90C26 90C33 90C46 PDFBibTeX XMLCite \textit{L. Bai} et al., Math. Program. 159, No. 1--2 (A), 109--136 (2016; Zbl 1346.90624) Full Text: DOI
Fan, Jinyan; Zhou, Anwa Computing the distance between the linear matrix pencil and the completely positive cone. (English) Zbl 1381.90064 Comput. Optim. Appl. 64, No. 3, 647-670 (2016). MSC: 90C22 15A22 15A23 44A60 90C26 90C59 65K05 PDFBibTeX XMLCite \textit{J. Fan} and \textit{A. Zhou}, Comput. Optim. Appl. 64, No. 3, 647--670 (2016; Zbl 1381.90064) Full Text: DOI
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu Extension of completely positive cone relaxation to moment cone relaxation for polynomial optimization. (English) Zbl 1336.90068 J. Optim. Theory Appl. 168, No. 3, 884-900 (2016). MSC: 90C20 90C25 90C26 PDFBibTeX XMLCite \textit{N. Arima} et al., J. Optim. Theory Appl. 168, No. 3, 884--900 (2016; Zbl 1336.90068) Full Text: DOI
Tono, Katsuya On LP-based approximation for copositive formulation of stable set problem. (English) Zbl 1421.90131 JSIAM Lett. 7, 69-72 (2015). MSC: 90C27 90C59 PDFBibTeX XMLCite \textit{K. Tono}, JSIAM Lett. 7, 69--72 (2015; Zbl 1421.90131) Full Text: DOI
Dong, Hongbo; Krislock, Nathan Semidefinite approaches for MIQCP: convex relaxations and practical methods. (English) Zbl 1369.90117 Defourny, Boris (ed.) et al., Modeling and optimization: theory and applications. MOPTA, Bethlehem, PA, USA, August 13–15, 2014. Selected contributions. Cham: Springer (ISBN 978-3-319-23698-8/hbk; 978-3-319-23699-5/ebook). Springer Proceedings in Mathematics & Statistics 147, 49-75 (2015). MSC: 90C22 90C11 90C26 PDFBibTeX XMLCite \textit{H. Dong} and \textit{N. Krislock}, Springer Proc. Math. Stat. 147, 49--75 (2015; Zbl 1369.90117) Full Text: DOI
Zhou, Anwa; Fan, Jinyan Interiors of completely positive cones. (English) Zbl 1342.65147 J. Glob. Optim. 63, No. 4, 653-675 (2015). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C05 90C22 90C25 PDFBibTeX XMLCite \textit{A. Zhou} and \textit{J. Fan}, J. Glob. Optim. 63, No. 4, 653--675 (2015; Zbl 1342.65147) Full Text: DOI arXiv
Sağol, Gizem; Yıldırım, E. Alper Analysis of copositive optimization based linear programming bounds on standard quadratic optimization. (English) Zbl 1321.90096 J. Glob. Optim. 63, No. 1, 37-59 (2015). MSC: 90C20 90C05 90C26 PDFBibTeX XMLCite \textit{G. Sağol} and \textit{E. A. Yıldırım}, J. Glob. Optim. 63, No. 1, 37--59 (2015; Zbl 1321.90096) Full Text: DOI Link
Lieder, Felix; Rad, Fatemeh Bani Asadi; Jarre, Florian Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques. (English) Zbl 1346.90603 Comput. Optim. Appl. 61, No. 3, 669-688 (2015). MSC: 90C09 90C22 PDFBibTeX XMLCite \textit{F. Lieder} et al., Comput. Optim. Appl. 61, No. 3, 669--688 (2015; Zbl 1346.90603) Full Text: DOI
de Klerk, Etienne; Laurent, Monique; Sun, Zhao An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution. (English) Zbl 1333.90104 SIAM J. Optim. 25, No. 3, 1498-1514 (2015). MSC: 90C26 90C30 PDFBibTeX XMLCite \textit{E. de Klerk} et al., SIAM J. Optim. 25, No. 3, 1498--1514 (2015; Zbl 1333.90104) Full Text: DOI arXiv
de Klerk, Etienne; Laurent, Monique; Sun, Zhao An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex. (English) Zbl 1328.90146 Math. Program. 151, No. 2 (B), 433-457 (2015). MSC: 90C30 90C60 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Math. Program. 151, No. 2 (B), 433--457 (2015; Zbl 1328.90146) Full Text: DOI arXiv
Peña, Javier; Vera, Juan C.; Zuluaga, Luis F. Completely positive reformulations for polynomial optimization. (English) Zbl 1328.90114 Math. Program. 151, No. 2 (B), 405-431 (2015). MSC: 90C26 90C20 PDFBibTeX XMLCite \textit{J. Peña} et al., Math. Program. 151, No. 2 (B), 405--431 (2015; Zbl 1328.90114) Full Text: DOI
de Klerk, Etienne; E.-Nagy, Marianna.; Sotirov, Renata; Truetsch, Uwe Symmetry in RLT-type relaxations for the quadratic assignment and standard quadratic optimization problems. (English) Zbl 1339.90203 Eur. J. Oper. Res. 233, No. 3, 488-499 (2014). MSC: 90B80 90C20 90C22 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Eur. J. Oper. Res. 233, No. 3, 488--499 (2014; Zbl 1339.90203) Full Text: DOI
Li, Xiaobo; Natarajan, Karthik; Teo, Chung-Piaw; Zheng, Zhichao Distributionally robust mixed integer linear programs: persistency models with applications. (English) Zbl 1339.90248 Eur. J. Oper. Res. 233, No. 3, 459-473 (2014). MSC: 90C11 90C31 90C20 PDFBibTeX XMLCite \textit{X. Li} et al., Eur. J. Oper. Res. 233, No. 3, 459--473 (2014; Zbl 1339.90248) Full Text: DOI Link
Sun, Zhao A refined error analysis for fixed-degree polynomial optimization over the simplex. (English) Zbl 1308.90172 J. Oper. Res. Soc. China 2, No. 3, 379-393 (2014). MSC: 90C30 90C60 PDFBibTeX XMLCite \textit{Z. Sun}, J. Oper. Res. Soc. China 2, No. 3, 379--393 (2014; Zbl 1308.90172) Full Text: DOI arXiv
Amaral, Paula; Bomze, Immanuel M.; Júdice, Joaquim Copositivity and constrained fractional quadratic problems. (English) Zbl 1312.90049 Math. Program. 146, No. 1-2 (A), 325-350 (2014). Reviewer: Francisco Guerra Vazquez (Puebla) MSC: 90C22 90C25 90C26 90C30 90C32 90C33 PDFBibTeX XMLCite \textit{P. Amaral} et al., Math. Program. 146, No. 1--2 (A), 325--350 (2014; Zbl 1312.90049) Full Text: DOI
Bomze, Immanuel M.; Gollowitzer, Stefan; Yıldırım, E. Alper Rounding on the standard simplex: regular grids for global optimization. (English) Zbl 1298.90076 J. Glob. Optim. 59, No. 2-3, 243-258 (2014). MSC: 90C26 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., J. Glob. Optim. 59, No. 2--3, 243--258 (2014; Zbl 1298.90076) Full Text: DOI Link
Lasserre, Jean B. New approximations for the cone of copositive matrices and its dual. (English) Zbl 1292.15034 Math. Program. 144, No. 1-2 (A), 265-276 (2014). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15B48 90C22 PDFBibTeX XMLCite \textit{J. B. Lasserre}, Math. Program. 144, No. 1--2 (A), 265--276 (2014; Zbl 1292.15034) Full Text: DOI arXiv
Sponsel, Julia; Dür, Mirjam Factorization and cutting planes for completely positive matrices by copositive projection. (English) Zbl 1286.90106 Math. Program. 143, No. 1-2 (A), 211-229 (2014). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{J. Sponsel} and \textit{M. Dür}, Math. Program. 143, No. 1--2 (A), 211--229 (2014; Zbl 1286.90106) Full Text: DOI
Billionnet, Alain Mathematical optimization ideas for biodiversity conservation. (English) Zbl 1317.90342 Eur. J. Oper. Res. 231, No. 3, 514-534 (2013). MSC: 90C90 92D40 90C09 PDFBibTeX XMLCite \textit{A. Billionnet}, Eur. J. Oper. Res. 231, No. 3, 514--534 (2013; Zbl 1317.90342) Full Text: DOI
Deng, Zhibin; Fang, Shu-Cherng; Jin, Qingwei; Xing, Wenxun Detecting copositivity of a symmetric matrix by an adaptive ellipsoid-based approximation scheme. (English) Zbl 1317.90229 Eur. J. Oper. Res. 229, No. 1, 21-28 (2013). MSC: 90C22 90C60 PDFBibTeX XMLCite \textit{Z. Deng} et al., Eur. J. Oper. Res. 229, No. 1, 21--28 (2013; Zbl 1317.90229) Full Text: DOI
Ahmed, Faizan; Dür, Mirjam; Still, Georg Copositive programming via semi-infinite optimization. (English) Zbl 1282.90203 J. Optim. Theory Appl. 159, No. 2, 322-340 (2013). MSC: 90C34 90C46 PDFBibTeX XMLCite \textit{F. Ahmed} et al., J. Optim. Theory Appl. 159, No. 2, 322--340 (2013; Zbl 1282.90203) Full Text: DOI
Dickinson, Peter J. C.; Dür, Mirjam; Gijben, Luuk; Hildebrand, Roland Scaling relationship between the copositive cone and Parrilo’s first level approximation. (English) Zbl 1282.15027 Optim. Lett. 7, No. 8, 1669-1679 (2013). MSC: 15B48 15A21 90C22 PDFBibTeX XMLCite \textit{P. J. C. Dickinson} et al., Optim. Lett. 7, No. 8, 1669--1679 (2013; Zbl 1282.15027) Full Text: DOI
Ahmed, Faizan; Still, Georg A note on set-semidefinite relaxations of nonconvex quadratic programs. (English) Zbl 1277.90084 J. Glob. Optim. 57, No. 4, 1139-1146 (2013). MSC: 90C20 90C22 90C09 PDFBibTeX XMLCite \textit{F. Ahmed} and \textit{G. Still}, J. Glob. Optim. 57, No. 4, 1139--1146 (2013; Zbl 1277.90084) Full Text: DOI
Chen, Xin; Peng, Jiming; Zhang, Shuzhong Sparse solutions to random standard quadratic optimization problems. (English) Zbl 1305.90323 Math. Program. 141, No. 1-2 (A), 273-293 (2013). Reviewer: Maxim Ivanov Todorov (San Andres Cholula) MSC: 90C20 90C26 60A99 PDFBibTeX XMLCite \textit{X. Chen} et al., Math. Program. 141, No. 1--2 (A), 273--293 (2013; Zbl 1305.90323) Full Text: DOI
Engau, Alexander; Anjos, Miguel F.; Bomze, Immanuel Constraint selection in a build-up interior-point cutting-plane method for solving relaxations of the stable-set problem. (English) Zbl 1272.90045 Math. Methods Oper. Res. 78, No. 1, 35-59 (2013). MSC: 90C22 90C51 90C09 90C20 90C27 90C35 90C90 PDFBibTeX XMLCite \textit{A. Engau} et al., Math. Methods Oper. Res. 78, No. 1, 35--59 (2013; Zbl 1272.90045) Full Text: DOI
Xia, Yong; Sheu, Ruey-Lin; Sun, Xiaoling; Li, Duan Tightening a copositive relaxation for standard quadratic optimization problems. (English) Zbl 1294.90044 Comput. Optim. Appl. 55, No. 2, 379-398 (2013). MSC: 90C20 90C22 90C46 PDFBibTeX XMLCite \textit{Y. Xia} et al., Comput. Optim. Appl. 55, No. 2, 379--398 (2013; Zbl 1294.90044) Full Text: DOI
Dong, Hongbo; Anstreicher, Kurt Separating doubly nonnegative and completely positive matrices. (English) Zbl 1263.90064 Math. Program. 137, No. 1-2 (A), 131-153 (2013). MSC: 90C26 90C22 90C20 15B48 PDFBibTeX XMLCite \textit{H. Dong} and \textit{K. Anstreicher}, Math. Program. 137, No. 1--2 (A), 131--153 (2013; Zbl 1263.90064) Full Text: DOI
Locatelli, Marco Approximation algorithm for a class of global optimization problems. (English) Zbl 1263.90066 J. Glob. Optim. 55, No. 1, 13-25 (2013). MSC: 90C26 90C59 PDFBibTeX XMLCite \textit{M. Locatelli}, J. Glob. Optim. 55, No. 1, 13--25 (2013; Zbl 1263.90066) Full Text: DOI
Burer, Samuel Copositive programming. (English) Zbl 1334.90098 Anjos, Miguel F. (ed.) et al., Handbook on semidefinite, conic and polynomial optimization. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). International Series in Operations Research & Management Science 166, 201-218 (2012). MSC: 90C22 90C05 90-01 PDFBibTeX XMLCite \textit{S. Burer}, Int. Ser. Oper. Res. Manag. Sci. 166, 201--218 (2012; Zbl 1334.90098) Full Text: DOI
Liu, Hairong; Yang, Xingwei; Latecki, Longin Jan; Yan, Shuicheng Dense neighborhoods on affinity graph. (English) Zbl 1254.68212 Int. J. Comput. Vis. 98, No. 1, 65-82 (2012). MSC: 68T05 68T10 68R10 PDFBibTeX XMLCite \textit{H. Liu} et al., Int. J. Comput. Vis. 98, No. 1, 65--82 (2012; Zbl 1254.68212) Full Text: DOI
Bomze, Immanuel M.; Locatelli, Marco Separable standard quadratic optimization problems. (English) Zbl 1254.90145 Optim. Lett. 6, No. 5, 857-866 (2012). MSC: 90C20 90C60 PDFBibTeX XMLCite \textit{I. M. Bomze} and \textit{M. Locatelli}, Optim. Lett. 6, No. 5, 857--866 (2012; Zbl 1254.90145) Full Text: DOI
Burer, Samuel; Dong, Hongbo Representing quadratically constrained quadratic programs as generalized copositive programs. (English) Zbl 1245.90080 Oper. Res. Lett. 40, No. 3, 203-206 (2012). MSC: 90C20 90C26 PDFBibTeX XMLCite \textit{S. Burer} and \textit{H. Dong}, Oper. Res. Lett. 40, No. 3, 203--206 (2012; Zbl 1245.90080) Full Text: DOI
Zhang, Xinzhen; Qi, Liqun; Ye, Yinyu The cubic spherical optimization problems. (English) Zbl 1252.65101 Math. Comput. 81, No. 279, 1513-1525 (2012). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65K05 90C60 90C20 65F20 PDFBibTeX XMLCite \textit{X. Zhang} et al., Math. Comput. 81, No. 279, 1513--1525 (2012; Zbl 1252.65101) Full Text: DOI
Sponsel, Julia; Bundfuss, Stefan; Dür, Mirjam An improved algorithm to test copositivity. (English) Zbl 1250.65061 J. Glob. Optim. 52, No. 3, 537-551 (2012). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 15A63 15B48 05C69 90C09 90C22 PDFBibTeX XMLCite \textit{J. Sponsel} et al., J. Glob. Optim. 52, No. 3, 537--551 (2012; Zbl 1250.65061) Full Text: DOI
Bomze, Immanuel M.; Schachinger, Werner; Uchida, Gabriele Think co(mpletely)positive! Matrix properties, examples and a clustered bibliography on copositive optimization. (English) Zbl 1268.90051 J. Glob. Optim. 52, No. 3, 423-445 (2012). MSC: 90C26 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., J. Glob. Optim. 52, No. 3, 423--445 (2012; Zbl 1268.90051) Full Text: DOI
Yıldırım, E. Alper On the accuracy of uniform polyhedral approximations of the copositive cone. (English) Zbl 1247.90215 Optim. Methods Softw. 27, No. 1, 155-173 (2012). MSC: 90C25 90C05 90C20 15B48 05C69 PDFBibTeX XMLCite \textit{E. A. Yıldırım}, Optim. Methods Softw. 27, No. 1, 155--173 (2012; Zbl 1247.90215) Full Text: DOI Link
Bomze, Immanuel M. Copositive optimization – recent developments and applications. (English) Zbl 1262.90129 Eur. J. Oper. Res. 216, No. 3, 509-520 (2012). Reviewer: Gabriela Cristescu (Arad) MSC: 90C25 90C33 90C46 PDFBibTeX XMLCite \textit{I. M. Bomze}, Eur. J. Oper. Res. 216, No. 3, 509--520 (2012; Zbl 1262.90129) Full Text: DOI
Hu, Qing-Jie; Ouyang, Zi-Sheng; Wang, Zhong-Mei Exceptional family and solvability of copositive complementarity problems. (English) Zbl 1233.90262 J. Math. Anal. Appl. 388, No. 1, 519-524 (2012). MSC: 90C33 PDFBibTeX XMLCite \textit{Q.-J. Hu} et al., J. Math. Anal. Appl. 388, No. 1, 519--524 (2012; Zbl 1233.90262) Full Text: DOI
Spadoni, Massimo; Stefanini, Luciano A differential evolution algorithm to deal with box, linear and quadratic-convex constraints for boundary optimization. (English) Zbl 1230.90157 J. Glob. Optim. 52, No. 1, 171-192 (2012). MSC: 90C26 PDFBibTeX XMLCite \textit{M. Spadoni} and \textit{L. Stefanini}, J. Glob. Optim. 52, No. 1, 171--192 (2012; Zbl 1230.90157) Full Text: DOI
Bao, Xiaowei; Sahinidis, Nikolaos V.; Tawarmalani, Mohit Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons. (English) Zbl 1232.49035 Math. Program. 129, No. 1 (B), 129-157 (2011). MSC: 49M29 65K05 90C22 90C26 90C30 PDFBibTeX XMLCite \textit{X. Bao} et al., Math. Program. 129, No. 1 (B), 129--157 (2011; Zbl 1232.49035) Full Text: DOI
Tardella, F. The fundamental theorem of linear programming: extensions and applications. (English) Zbl 1219.90120 Optimization 60, No. 1-3, 283-301 (2011). MSC: 90C20 90C26 90C27 90C35 PDFBibTeX XMLCite \textit{F. Tardella}, Optimization 60, No. 1--3, 283--301 (2011; Zbl 1219.90120) Full Text: DOI
Zheng, X. J.; Sun, X. L.; Li, D. Separable relaxation for nonconvex quadratic integer programming: Integer diagonalization approach. (English) Zbl 1198.90299 J. Optim. Theory Appl. 146, No. 2, 463-489 (2010). MSC: 90C10 90C20 90C26 PDFBibTeX XMLCite \textit{X. J. Zheng} et al., J. Optim. Theory Appl. 146, No. 2, 463--489 (2010; Zbl 1198.90299) Full Text: DOI
Anstreicher, Kurt M.; Burer, Samuel Computable representations for convex hulls of low-dimensional quadratic forms. (English) Zbl 1198.90311 Math. Program. 124, No. 1-2 (B), 33-43 (2010). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{K. M. Anstreicher} and \textit{S. Burer}, Math. Program. 124, No. 1--2 (B), 33--43 (2010; Zbl 1198.90311) Full Text: DOI Link
Burer, Samuel Optimizing a polyhedral-semidefinite relaxation of completely positive programs. (English) Zbl 1190.90135 Math. Program. Comput. 2, No. 1, 1-19 (2010). MSC: 90C26 90C05 90C22 PDFBibTeX XMLCite \textit{S. Burer}, Math. Program. Comput. 2, No. 1, 1--19 (2010; Zbl 1190.90135) Full Text: DOI
Kontogiannis, Spyros C.; Spirakis, Paul G. Well supported approximate equilibria in bimatrix games. (English) Zbl 1200.91012 Algorithmica 57, No. 4, 653-667 (2010). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 91A05 90C08 90C33 90C59 90C60 PDFBibTeX XMLCite \textit{S. C. Kontogiannis} and \textit{P. G. Spirakis}, Algorithmica 57, No. 4, 653--667 (2010; Zbl 1200.91012) Full Text: DOI
Bomze, Immanuel M.; Schachinger, Werner Multi-standard quadratic optimization: Interior point methods and cone programming reformulation. (English) Zbl 1187.90210 Comput. Optim. Appl. 45, No. 2, 237-256 (2010). MSC: 90C20 90C51 PDFBibTeX XMLCite \textit{I. M. Bomze} and \textit{W. Schachinger}, Comput. Optim. Appl. 45, No. 2, 237--256 (2010; Zbl 1187.90210) Full Text: DOI
Eichfelder, Gabriele; Jahn, Johannes Foundations of set-semidefinite optimization. (English) Zbl 1181.90213 Pardalos, Panos M. (ed.) et al., Nonlinear analysis and variational problems. In Honor of George Isac. Berlin: Springer (ISBN 978-1-4419-0157-6/hbk; 978-1-4419-0158-3/ebook). Springer Optimization and Its Applications 35, 259-284 (2010). MSC: 90C22 PDFBibTeX XMLCite \textit{G. Eichfelder} and \textit{J. Jahn}, Springer Optim. Appl. 35, 259--284 (2010; Zbl 1181.90213) Full Text: DOI
Dukanovic, Igor; Rendl, Franz Copositive programming motivated bounds on the stability and the chromatic numbers. (English) Zbl 1194.90109 Math. Program. 121, No. 2 (A), 249-268 (2010). Reviewer: Svetlana A. Kravchenko (Minsk) MSC: 90C35 90C22 05C15 PDFBibTeX XMLCite \textit{I. Dukanovic} and \textit{F. Rendl}, Math. Program. 121, No. 2 (A), 249--268 (2010; Zbl 1194.90109) Full Text: DOI
Burer, Samuel On the copositive representation of binary and continuous nonconvex quadratic programs. (English) Zbl 1180.90234 Math. Program. 120, No. 2 (A), 479-495 (2009). MSC: 90C25 90C26 90C20 PDFBibTeX XMLCite \textit{S. Burer}, Math. Program. 120, No. 2 (A), 479--495 (2009; Zbl 1180.90234) Full Text: DOI
Locatelli, M. Complexity results for some global optimization problems. (English) Zbl 1173.90545 J. Optim. Theory Appl. 140, No. 1, 93-102 (2009). MSC: 90C30 90C60 PDFBibTeX XMLCite \textit{M. Locatelli}, J. Optim. Theory Appl. 140, No. 1, 93--102 (2009; Zbl 1173.90545) Full Text: DOI
Iusem, Alfredo; Seeger, Alberto Searching for critical angles in a convex cone. (English) Zbl 1163.52003 Math. Program. 120, No. 1 (B), 3-25 (2009). MSC: 52A40 90C26 PDFBibTeX XMLCite \textit{A. Iusem} and \textit{A. Seeger}, Math. Program. 120, No. 1 (B), 3--25 (2009; Zbl 1163.52003) Full Text: DOI
Scozzari, Andrea; Tardella, Fabio A clique algorithm for standard quadratic programming. (English) Zbl 1163.90691 Discrete Appl. Math. 156, No. 13, 2439-2448 (2008). MSC: 90C20 05C35 05C85 PDFBibTeX XMLCite \textit{A. Scozzari} and \textit{F. Tardella}, Discrete Appl. Math. 156, No. 13, 2439--2448 (2008; Zbl 1163.90691) Full Text: DOI
De Klerk, Etienne The complexity of optimizing over a simplex, hypercube or sphere: a short survey. (English) Zbl 1152.90607 CEJOR, Cent. Eur. J. Oper. Res. 16, No. 2, 111-125 (2008). MSC: 90C30 90C60 68Q25 PDFBibTeX XMLCite \textit{E. De Klerk}, CEJOR, Cent. Eur. J. Oper. Res. 16, No. 2, 111--125 (2008; Zbl 1152.90607) Full Text: DOI
Peña, Javier F.; Vera, Juan C.; Zuluaga, Luis F. Exploiting equalities in polynomial programming. (English) Zbl 1163.90755 Oper. Res. Lett. 36, No. 2, 223-228 (2008). MSC: 90C30 90C09 PDFBibTeX XMLCite \textit{J. F. Peña} et al., Oper. Res. Lett. 36, No. 2, 223--228 (2008; Zbl 1163.90755) Full Text: DOI