Inexact Methods For Large-Scale Stochastic Programming
Year: 2024
Type: article
Abstract: This dissertation addresses the development of inexact methods for solving large-scale stochastic programming problems, with a focus on two-stage and multistage settings. Stochastic programming is a robust approach for managing uncertainty in decision-making, with applications across various domains like supply chain management, power systems, and logistics. However, solving large-scale stochastic programming problems, especially those with a nonlinear structure, is computationally challenging due to the high-dimensional nature of uncertainties and the need for efficient optimization techniques. This work introduces novel inexact proximal bundle algorithms designed to solve two-stage stochastic quadratic programming problems. The proposed methods utilize dual-based and partition-based approaches to approximate the second-stage solution, significantly reducing the computational burden compared to traditional exact algorithms. Asymptotic convergence properties are established, and the algorithms' efficiency is demonstrated through numerical experiments on instances such as the optimal power flow problem. The study also includes a rigorous analysis of how inexact approximations impact convergence rates, offering insights into improving solution accuracy and efficiency. Additionally, this dissertation explores multistage SP models where uncertainties follow a Markov process. A regularized stochastic dual dynamic programming method is adapted for cases where the probability distributions are not known in advance, enabling data-driven optimization through sequential sampling. The effectiveness of the proposed approaches is validated through implementation and performance evaluation, highlighting their potential for real-world applications.
Author: Fadavi, Niloofar
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7029249898
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