Employing the Mean Extra-Gradient Approach to Solve the Optimal Transport Problem
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Abstract
The Optimal Transport Problem (OTP) serves as a cornerstone in the optimization landscape, seeking the most cost-effective strategy to transport mass from one distribution to another. In this article, we explore a cutting-edge methodology for addressing the complexities inherent in the OTP — the Mean Extra-Gradient Approach. This iterative optimization method utilizes the extra-gradient of the cost functional to refine the transport plan, offering a versatile and powerful toolset for solving real-world transportation and distribution challenges. Through a detailed examination of theoretical foundations, practical applications, and potential future directions, this article provides a comprehensive overview of employing the Mean Extra-Gradient Approach to unlock new insights and advancements in solving the Optimal Transport Problem.