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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. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    3. 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.
    4. 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.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    7. 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.
    8. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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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