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

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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.

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Authors and Affiliations

  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, China

    Jia-Wang Nie & Ya-Xiang Yuan

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  1. Jia-Wang Nie
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  2. Ya-Xiang Yuan
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Nie, JW., Yuan, YX. A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps. Annals of Operations Research 103, 115–133 (2001). https://doi.org/10.1023/A:1012994820412

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