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Properties of two DC algorithms in quadratic programming

Author

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  • Hoai Le Thi
  • Tao Pham Dinh
  • Nguyen Yen

Abstract

Some new properties of the Projection DC decomposition algorithm (we call it Algorithm A) and the Proximal DC decomposition algorithm (we call it Algorithm B) Pham Dinh et al. in Optim Methods Softw, 23(4): 609–629 (2008) for solving the indefinite quadratic programming problem under linear constraints are proved in this paper. Among other things, we show that DCA sequences generated by Algorithm A converge to a locally unique solution if the initial points are taken from a neighborhood of it, and DCA sequences generated by either Algorithm A or Algorithm B are all bounded if a condition guaranteeing the solution existence of the given problem is satisfied. Copyright Springer Science+Business Media, LLC. 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:3:p:481-495
    DOI: 10.1007/s10898-010-9573-1
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    Cited by:

    1. Nguyen Qui, 2013. "Variational inequalities over Euclidean balls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 243-258, October.
    2. Duong Thi Viet An, 2022. "Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 426-442, February.
    3. 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.
    4. Nguyen Thanh Qui, 2016. "Coderivatives of implicit multifunctions and stability of variational systems," Journal of Global Optimization, Springer, vol. 65(3), pages 615-635, July.
    5. Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
    6. Bui Ngoc Muoi & Nguyen Dong Yen, 2017. "Local Stability and Local Convergence of the Basic Trust-Region Method," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 578-593, February.

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