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A block active set algorithm for large-scalequadratic programming with box constraints

Author

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  • L. Fernandes
  • A. Fischer
  • J. Júdice
  • C. Requejo
  • J. Soares

Abstract

An algorithm for computing a stationary point of a quadratic program with box constraints(BQP) is proposed. Each iteration of this procedure comprises a guessing strategy whichforecasts the active bounds at a stationary point, the determination of a descent direction bymeans of solving a reduced strictly convex quadratic program with box constraints and anexact line search. Global convergence is established in the sense that every accumulationpoint is stationary. Moreover, it is shown that the algorithm terminates after a finite numberof iterations, if at least one iterate is sufficiently close to a stationary point which satisfiesa certain sufficient optimality condition. The algorithm can be easily implemented for sparselarge-scale BQPs. Furthermore, it simplifies for concave BQPs, as it is not required to solvestrictly convex quadratic programs in this case. Computational experience with large-scaleBQPs is included and shows the appropriateness of this type of methodology. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:81:y:1998:i:0:p:75-96:10.1023/a:1018990014974
    DOI: 10.1023/A:1018990014974
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    Cited by:

    1. Zdeněk Dostál & Lukáš Pospíšil, 2016. "Optimal iterative QP and QPQC algorithms," Annals of Operations Research, Springer, vol. 243(1), pages 5-18, August.
    2. Che Xu & Wenjun Chang & Weiyong Liu, 2023. "Data-driven decision model based on local two-stage weighted ensemble learning," Annals of Operations Research, Springer, vol. 325(2), pages 995-1028, June.
    3. 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.
    4. Danielson, Mats & Ekenberg, Love, 2007. "Computing upper and lower bounds in interval decision trees," European Journal of Operational Research, Elsevier, vol. 181(2), pages 808-816, September.
    5. 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.
    6. 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.

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