Article Contents
Article Contents

# Statistical inference of semidefinite programming with multiple parameters

• * Corresponding author: Jiani Wang

Jiani Wang is supported by NNSFC grant Nos. 11571059, 11731013 and 91330206

• The parameters in the semidefinite programming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical properties of estimates of the optimal value and the optimal solutions are given in this paper, when the estimated parameters are both in the objective function and in the constraints. This analysis is mainly based on the theory of the linear programming and the perturbation theory of the semidefinite programming.

Mathematics Subject Classification: Primary: 90C22, 90C31, 90C46; Secondary: 62D05, 62F12.

 Citation:

• Table 1.  $\hat{\vartheta}_N$ in the case that the optimal solution is not unique

 N Bias SD SE CP 100 -0.01575607 0.09802304 0.1026943 0.959 300 -0.008588234 0.05875263 0.05928791 0.947 800 -0.005730269 0.03494695 0.03630683 0.953

Table 2.  $\hat{\vartheta}_N$ with the unique optimal solution

 N Bias SD SE CP 100 -0.008575782 0.2752905 0.283196 0.954 300 0.000433069 0.1598366 0.1635033 0.953 800 0.002228357 0.1022441 0.1001249 0.948

Table 3.  $\hat{x}_N$ with the unique optimal solution

 N x Bias SD SE CP 100 $x_1$ 0.001119686 0.1960365 0.2006396 0.956 $x_2$ -0.005239017 0.2040734 0.2006396 0.951 400 $x_1$ 0.003114901 0.09937129 0.1003198 0.948 $x_2$ 0.004845715 0.1005173 0.1003198 0.946 1000 $x_1$ -0.0001884376 0.06216153 0.06344781 0.943 $x_2$ 0.005075925 0.06360439 0.06344781 0.952
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