Statistical inference of semidefinite programming with multiple parameters. (English) Zbl 1449.90282
Summary: 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.
MSC:
| 90C22 | Semidefinite programming |
| 90C31 | Sensitivity, stability, parametric optimization |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C05 | Linear programming |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
linear semidefinite programming; multiple parameters; linear operator theory; constraint nondegeneracy; statistical inference; asymptoticsReferences:
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