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A hybrid direction algorithm for solving a convex quadratic problem

Author

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  • Mohand Ouamer Bibi
  • Nacira Ikheneche
  • Mohand Bentobache

Abstract

In this paper, we propose a new algorithm for solving convex quadratic programming problems with bounded variables. Instead of using the standard direction of the adaptive method, which is constructed by minimising only the linear part of the objective function increment, we will suggest a new descent direction, called 'hybrid direction'. This latter is constructed by minimising a quadratic part of the increment. Furthermore, we define a quantity called 'optimality estimate' from which we derive sufficient and necessary conditions of optimality. On the basis of this new concept, we construct an algorithm for solving convex quadratic programs. In order to compare our method with the active-set method implemented in MATLAB, numerical experiments on randomly generated test problems are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:ids:ijmore:v:16:y:2020:i:2:p:159-178
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    Citations

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    Cited by:

    1. 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.
    2. 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.

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