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Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming

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  • Hoang Ngoc Tuan

    (Hanoi Pedagogical University)

Abstract

We prove that any iterative sequence generated by the projection decomposition algorithm of Pham Dinh et al. (Optim Methods Softw 23:609–629, 2008) in quadratic programming is bounded, provided that the quadratic program in question is two-dimensional and solvable.

Suggested Citation

  • Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0530-x
    DOI: 10.1007/s10957-014-0530-x
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2012. "Behavior of DCA sequences for solving the trust-region subproblem," Journal of Global Optimization, Springer, vol. 53(2), pages 317-329, June.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. Hoai Le Thi & Tao Pham Dinh & Nguyen Yen, 2011. "Properties of two DC algorithms in quadratic programming," Journal of Global Optimization, Springer, vol. 49(3), pages 481-495, March.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    6. Hoang Ngoc Tuan, 2012. "Convergence Rate of the Pham Dinh–Le Thi Algorithm for the Trust-Region Subproblem," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 904-915, September.
    7. G. M. Lee & N. N. Tam & N. D. Yen, 2006. "Continuity of the Solution Map in Quadratic Programs under Linear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 415-423, June.
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