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Bi-affine scaling iterative method for convex quadratic programming with bound constraints

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  • Yue, Hongwei
  • Shen, Peiping

Abstract

To solve general convex quadratic programming problems with bound constraints, this paper proposes a new interior point iterative method that is easy to be implemented. The method exhibits a simple and sufficiently smooth search direction, and possesses the characteristics of affine scaling. Under the limited optimal stepsize rule, starting from an arbitrary interior point, any accumulation point of the generated sequence is an optimal solution of the corresponding problem. Furthermore, due to the absence of introducing dual variables and solving equations, the proposed method is more suitable for solving large-scale problems. Preliminary numerical results indicate that the new method has advantages in terms of both efficiency and accuracy.

Suggested Citation

  • Yue, Hongwei & Shen, Peiping, 2024. "Bi-affine scaling iterative method for convex quadratic programming with bound constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 373-382.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:373-382
    DOI: 10.1016/j.matcom.2024.07.013
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    References listed on IDEAS

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    1. S. Cafieri & M. D’Apuzzo & M. Marino & A. Mucherino & G. Toraldo, 2006. "Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 55-75, April.
    2. Y. S. Xia & J. Wang, 2000. "On the Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 129-150, July.
    3. L. Z. Liao, 2005. "A Continuous Method for Convex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 207-226, January.
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