ASYMPTOTICS OF THE OPTIMAL VALUE OF SAA WITH AMIS ON MINIMAX STOCHASTIC PROGRAMS

Wenjin Zhang

doi:10.11948/20240378

2025 Volume 15 Issue 2

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Wenjin Zhang. ASYMPTOTICS OF THE OPTIMAL VALUE OF SAA WITH AMIS ON MINIMAX STOCHASTIC PROGRAMS[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1203-1215. doi: 10.11948/20240378

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Wenjin Zhang. ASYMPTOTICS OF THE OPTIMAL VALUE OF SAA WITH AMIS ON MINIMAX STOCHASTIC PROGRAMS[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 1203-1215. doi: 10.11948/20240378

ASYMPTOTICS OF THE OPTIMAL VALUE OF SAA WITH AMIS ON MINIMAX STOCHASTIC PROGRAMS

Wenjin Zhang^1, ,

1.
College of Mathematics, Jilin University, Changchun 130012, China

Corresponding author: Email: zhangwenjinmails@163.com(W. Zhang)

Abstract

Abstract

The minimax stochastic programming problem is approximated in this paper using the sample average approximation with adaptive multiple importance sampling. We discuss the asymptotics and convergence of its optimal value. The core is the research and utilization of martingale difference sequences. The functional central limit theorem for martingale difference sequences is one of the main tools in studying the asymptotics. Finally, we apply this result to discuss a risk averse optimization problem.
- Adaptive multiple importance sampling /
- minimax stochastic programming /
- martingale difference sequence /
- central limit theorem
MSC: 90C15, 90C47

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References

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