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A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps

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  • Jia-Wang Nie
  • Ya-Xiang Yuan

Abstract

Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor–corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K 0 , we use Dikin-type step. Otherwise, Newton centering step is taken. In both cases, step-length is determined by line search. We show that at least a constant reduction in the potential function is guaranteed. Moreover the algorithm is proved to terminate in O $$(\sqrt n $$ log (1/ε)) steps. In the end of this paper, we discuss how to compute search direction (ΔX,ΔS) using the conjugate gradient method. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Jia-Wang Nie & Ya-Xiang Yuan, 2001. "A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps," Annals of Operations Research, Springer, vol. 103(1), pages 115-133, March.
    • Handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:115-133:10.1023/a:1012994820412
    DOI: 10.1023/A:1012994820412
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    Cited by:

    1. Sun, Jie & Zhang, Su, 2010. "A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1210-1220, December.
    2. Houduo Qi, 2009. "Local Duality of Nonlinear Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 124-141, February.
    3. Baha Alzalg & Asma Gafour, 2023. "Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 490-515, February.
    4. Huiling Lin, 2012. "An inexact spectral bundle method for convex quadratic semidefinite programming," Computational Optimization and Applications, Springer, vol. 53(1), pages 45-89, September.

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