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Nonconvex quadratically constrained quadratic programming: best D.C. decompositions and their SDP representations

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  • X. Zheng
  • X. Sun
  • D. Li

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  • X. Zheng & X. Sun & D. Li, 2011. "Nonconvex quadratically constrained quadratic programming: best D.C. decompositions and their SDP representations," Journal of Global Optimization, Springer, vol. 50(4), pages 695-712, August.
    • Handle: RePEc:spr:jglopt:v:50:y:2011:i:4:p:695-712
    DOI: 10.1007/s10898-010-9630-9
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    1. B. Kalantari & J. B. Rosen, 1987. "An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 544-561, August.
    2. A. T. Phillips & J. B. Rosen, 1990. "Guaranteed ϵ‐approximate solution for indefinite quadratic global minimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 499-514, August.
    3. Le Thi Hoai An & Pham Dinh Tao & Le Dung Muu, 1998. "A Combined D.C. Optimization—Ellipsoidal Branch-and-Bound Algorithm for Solving Nonconvex Quadratic Programming Problems," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 9-28, March.
    4. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    2. Wang, Xiaotian & Wang, Xin, 2019. "Flexible parking reservation system and pricing: A continuum approximation approach," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 408-434.
    3. Shinji Yamada & Akiko Takeda, 2018. "Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization," Journal of Global Optimization, Springer, vol. 71(2), pages 313-339, June.
    4. Xiaojin Zheng & Yutong Pan & Xueting Cui, 2018. "Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint," Journal of Global Optimization, Springer, vol. 70(4), pages 719-735, April.
    5. Jianzhe Zhen & Ahmadreza Marandi & Danique de Moor & Dick den Hertog & Lieven Vandenberghe, 2022. "Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2410-2427, September.
    6. Mohammad Keyanpour & Naser Osmanpour, 2018. "On solving quadratically constrained quadratic programming problem with one non-convex constraint," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 320-336, June.
    7. Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.
    8. Xiaodong Ding & Hezhi Luo & Huixian Wu & Jianzhen Liu, 2021. "An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation," Computational Optimization and Applications, Springer, vol. 80(1), pages 89-120, September.
    9. Samuel Burer & Sunyoung Kim & Masakazu Kojima, 2014. "Faster, but weaker, relaxations for quadratically constrained quadratic programs," Computational Optimization and Applications, Springer, vol. 59(1), pages 27-45, October.
    10. Marandi, Ahmadreza, 2017. "Aspects of quadratic optimization - nonconvexity, uncertainty, and applications," Other publications TiSEM d2b9c576-7128-4ee4-939a-7, Tilburg University, School of Economics and Management.
    11. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.
    12. Marcia Fampa & Jon Lee & Wendel Melo, 2017. "On global optimization with indefinite quadratics," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 309-337, September.
    13. Hezhi Luo & Xiaodi Bai & Jiming Peng, 2019. "Enhancing Semidefinite Relaxation for Quadratically Constrained Quadratic Programming via Penalty Methods," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 964-992, March.

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