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Partial Sample Average Approximation Method for Chance Constrained Programs

Program in Applied Mathematics Colloquium

Partial Sample Average Approximation Method for Chance Constrained Programs
Series: Program in Applied Mathematics Colloquium
Location: MATH 501
Presenter: Jianqiang Cheng, Systems and Industrial Engineering, University of Arizona

In this talk, we present a new scheme of a sampling-based method, named Partial Sample Average Approximation (PSAA) method, to solve chance constrained programs. In contrast to Sample Average Approximation (SAA) which samples all of the random variables, PSAA only samples a portion of random variables by making use of the independence of some of the random variables for stepwise evaluation of the expectation. The main advantage of the proposed approach is that the PSAA approximation problem contains only continuous auxiliary variables, whilst the SAA reformulation contains binary ones. Moreover, we prove that the proposed approach has the same convergence properties as SAA. At the end, a numerical study on different applications shows the strengths of the proposed approach, in comparison with other popular approaches, such as SAA and scenario approach.