An algorithm for the calculation of upper variance under multiple probabilities and its application to quadratic programming

Abstract

The concept of upper variance under multiple probabilities is defined through a corresponding minimax optimization problem. This study proposes a simple algorithm to solve this optimization problem exactly. Additionally, we provide a probabilistic representation for a class of quadratic programming problems, demonstrating the practical application of our approach.

Keywords

Multiple probabilities / Quadratic programming / Sublinear expectation / Upper variance

Acknowledgements

This work is supported by the NSF of China (Grant Nos. 12326603 and 11601281), NSF of Shandong Province (Grant No. ZR2021MA018), National Key R&D Program of China (Grant No.2018YFA0703900), the Qilu Young Scholars Program of Shandong University, and the Fundamental Research Funds for the Central Universities.

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