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

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 K0, 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(p n log(1==)) steps. In the end of this paper, we discuss how to compute search direction ((X; S) using the conjugate gradient method.