IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v192y2022i1d10.1007_s10957-021-01980-2.html
   My bibliography  Save this article

Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems

Author

Listed:
  • Amar Andjouh

    (Faculty of the Exact Sciences, University of Bejaia)

  • Mohand Ouamer Bibi

    (Faculty of the Exact Sciences, University of Bejaia)

Abstract

In this paper, we propose a new adaptive method for solving the non-convex quadratic minimization problem subject to box constraints, where the associated matrix is indefinite, in particular with one negative eigenvalue. We investigate the derived sufficient global optimality conditions by exploiting the particular form of the Moreau envelope (L-subdifferential) of the quadratic function and abstract convexity, also to develop a new algorithm for solving the original problem without transforming it, that we call adaptive global algorithm, which can effectively find one global minimizer of the problem. Furthermore, the research of the convex support of the objective function allows us to characterize the global optimum and reduce the complexity of the big size problems. We give some theoretical aspects of global optimization and present numerical examples with test problems for illustrating our approach.

Suggested Citation

  • Amar Andjouh & Mohand Ouamer Bibi, 2022. "Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 360-378, January.
  • Handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01980-2
    DOI: 10.1007/s10957-021-01980-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01980-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-021-01980-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mohand Ouamer Bibi & Nacira Ikheneche & Mohand Bentobache, 2020. "A hybrid direction algorithm for solving a convex quadratic problem," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(2), pages 159-178.
    2. M. Ç. Pinar, 2004. "Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 433-440, August.
    3. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    4. Niu, Yi-Shuai & Júdice, Joaquim & Le Thi, Hoai An & Pham, Dinh Tao, 2019. "Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 95-113.
    5. 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.
    6. Hoai An Le Thi & Van Ngai Huynh & Tao Pham Dinh, 2018. "Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 103-126, October.
    7. V. Jeyakumar & A. M. Rubinov & Z. Y. Wu, 2007. "Generalized Fenchel’s Conjugation Formulas and Duality for Abstract Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 441-458, March.
    8. L. Fernandes & A. Fischer & J. Júdice & C. Requejo & J. Soares, 1998. "A block active set algorithm for large-scalequadratic programming with box constraints," Annals of Operations Research, Springer, vol. 81(0), pages 75-96, June.
    9. Riccardo Cambini & Claudio Sodini, 2008. "A sequential method for a class of box constrained quadratic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 223-243, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xue-Gang Zhou & Xiao-Peng Yang & Bing-Yuan Cao, 2015. "Global optimality conditions for cubic minimization problems with cubic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 243-264, December.
    2. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    3. Guoyin Li, 2012. "Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 710-726, March.
    4. Min Tao & Jiang-Ning Li, 2023. "Error Bound and Isocost Imply Linear Convergence of DCA-Based Algorithms to D-Stationarity," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 205-232, April.
    5. 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.
    6. Hoai An Le Thi & Van Ngai Huynh & Tao Pham Dinh, 2018. "Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 103-126, October.
    7. Thai Doan Chuong, 2020. "Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 289-299, April.
    8. Riccardo Cambini & Giovanna D’Inverno, 2024. "Rank-two programs involving linear fractional functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 299-325, June.
    9. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    10. M. V. Dolgopolik, 2023. "DC semidefinite programming and cone constrained DC optimization II: local search methods," Computational Optimization and Applications, Springer, vol. 85(3), pages 993-1031, July.
    11. H. Mohebi & J.-E. Martínez-Legaz & M. Rocco, 2012. "Some criteria for maximal abstract monotonicity," Journal of Global Optimization, Springer, vol. 53(2), pages 137-163, June.
    12. X. Zheng & X. Sun & D. Li & Y. Xu, 2012. "On zero duality gap in nonconvex quadratic programming problems," Journal of Global Optimization, Springer, vol. 52(2), pages 229-242, February.
    13. Chaoli Yao & Shengjie Li, 2018. "Vector Topical Function, Abstract Convexity and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 717-742, June.
    14. Panigrahi, Paresh Kumar & Nayak, Sukanta, 2024. "Numerical approach to solve imprecisely defined systems using Inner Outer Direct Search optimization technique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 578-606.
    15. Hoai An Thi & Thi Minh Tam Nguyen & Tao Pham Dinh, 2023. "On solving difference of convex functions programs with linear complementarity constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 163-197, September.
    16. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2020. "An active-set algorithmic framework for non-convex optimization problems over the simplex," Computational Optimization and Applications, Springer, vol. 77(1), pages 57-89, September.
    17. Z. Y. Wu & Y. J. Yang & F. S. Bai & M. Mammadov, 2011. "Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 241-259, November.
    18. Hongbo Dong & Min Tao, 2021. "On the Linear Convergence to Weak/Standard d-Stationary Points of DCA-Based Algorithms for Structured Nonsmooth DC Programming," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 190-220, April.
    19. Brás, Carmo P. & Fischer, Andreas & Júdice, Joaquim J. & Schönefeld, Klaus & Seifert, Sarah, 2017. "A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 36-48.
    20. Elimhan N. Mahmudov, 2020. "Infimal Convolution and Duality in Problems with Third-Order Discrete and Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 781-809, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:192:y:2022:i:1:d:10.1007_s10957-021-01980-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.