Dual Formulation

Dual formulation is a mathematical approach used to reformulate optimization problems, often leading to more efficient solutions or enhanced robustness to noise. Current research focuses on applying dual formulations to diverse areas, including optimal transport problems, PDE discovery from noisy data, and machine learning tasks like K-means clustering and high-order dependency parsing, often employing algorithms like Sinkhorn iterations or dual decomposition. This technique's significance lies in its ability to improve the efficiency and accuracy of solving complex problems across various scientific disciplines and engineering applications, particularly those involving large datasets or noisy measurements.